WO2022237196A1 - Cluster-state-based terminal-selectable method and system for remotely preparing two-bit state - Google Patents

Cluster-state-based terminal-selectable method and system for remotely preparing two-bit state Download PDF

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WO2022237196A1
WO2022237196A1 PCT/CN2021/143112 CN2021143112W WO2022237196A1 WO 2022237196 A1 WO2022237196 A1 WO 2022237196A1 CN 2021143112 W CN2021143112 W CN 2021143112W WO 2022237196 A1 WO2022237196 A1 WO 2022237196A1
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receiving user
user
target receiving
target
information
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PCT/CN2021/143112
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French (fr)
Chinese (zh)
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姜敏
苗天宇
汪澳
龚仁智
黄旭
李太超
陈虹
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苏州大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding

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  • the invention relates to the technical field of optical communication network and information dissemination, in particular to a method and system for optionally remotely preparing two-bit states by terminals based on cluster states.
  • quantum communication network is based on the quantum key distribution between nodes in the communication network, so that the communication parties in the network can exchange the theory accurately secure key.
  • quantum repeaters are generally used as the intermediate nodes in the network.
  • a chain channel can be formed, and then the particles held by the terminal nodes and the relay nodes in the network are divided into The Bell measurement operation is implemented, and finally the unknown quantum state to be transmitted is "restored" on the particles held by the destination node, and the communication between two communication nodes can be finally realized based on the EPR protocol.
  • quantum state remote preparation schemes have emerged.
  • quantum remote state preparation communication schemes are realized based on the conditions of the sending user and the receiving user, and there is a lack of quantum state remote preparation schemes under the optional situation of the receiving user.
  • Cluster state is a new type of multi-particle entangled state. Compared with other types of entangled states, it has stronger stability and anti-interference, and has the entanglement characteristics of GHZ state and W state at the same time. It has been widely used in quantum in recent years. Research fields such as computing, quantum secure direct communication (QSDC) and remote preparation of quantum states. In 2016, it was proposed to theoretically realize the remote preparation of four-bit cluster states, and the probability of success depends on the coefficient of the entangled state of the quantum channel. Subsequently, in 2017, it was proposed to realize the preparation of any multi-bit state based on n maximum entangled two-bit quantum states.
  • QSDC quantum secure direct communication
  • the technical problem to be solved by the present invention is to overcome the defects in the prior art that there is no quantum communication scheme under the optional situation of the receiving user and that the communication quality is affected by the bit error of the channel bit so that it does not meet the requirements of the actual communication scene.
  • the present invention provides a method for optional remote preparation of a two-bit state based on a terminal in a cluster state.
  • the system includes a sending user, a receiving user edge node, and multiple candidate receiving users.
  • the method includes:
  • the target receiving user among multiple candidate receiving users is determined, the sending user remotely prepares the information to be transmitted for the target receiving user, and the base measurement operation is performed by the non-target receiving user, and the measured The result is sent to the target receiving user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements;
  • the target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
  • determining the direct entanglement channel between the sending user and the receiving user edge node includes:
  • the sending user and each intermediate node perform CZ operation on the held particles respectively, and the intermediate node performs Bell measurement on the held particles, and sends the measurement result to the sending user, and the sending user determines its relationship with the receiving user according to the measurement result Direct entanglement channels between edge nodes.
  • the intermediate node when the intermediate node sends the Bell measurement result to the sending user, the intermediate node sends the channel bit error information to the sending user, and the sending user The information determines the channel matrix that constitutes direct quantum communication.
  • the non-maximally entangled cluster state channel is used for connection between the edge node of the sending user and the receiving user.
  • determining the GHZ channel between the receiving user edge node and multiple candidate receiving users includes:
  • the receiving user edge node performs CZ operation, CNOT operation and base measurement on the held particles, and sends the measurement results to the candidate receiving user, and the candidate receiving user performs unitary operation on the held particles, and A GHZ channel is constructed between the receiving user edge node and multiple candidate receiving users.
  • the edge node of the receiving user is connected to multiple candidate receiving users using a maximum entangled cluster state channel.
  • the target receiving user performs a unitary operation according to the measurement results of the non-target receiving user, and restoring the information to be transmitted includes:
  • the target receiving user can directly recover the information to be transmitted; if the measurement result of the non-target receiving user on the particle is not
  • the present invention also provides a method for the sending user to perform optional remote preparation of a two-bit state based on the terminal of the cluster state, including:
  • While constructing the direct entanglement channel determine the target receiving user among multiple candidate receiving users, remotely prepare the information to be transmitted for the target receiving user, construct a matrix according to the information to be transmitted, and perform matrix operation and measurement, among which the non-target
  • the receiving user performs base measurement operations, and sends the measurement results to the target receiving user, and the target receiving user performs matrix operations on the particles held, and performs unitary operations according to the measurement results of non-target receiving users, and restores Information to be sent.
  • the present invention also provides a method for candidate receiving users to perform terminal optional remote preparation of two-bit states based on cluster states, including:
  • the target receiving user determined while constructing the direct entanglement channel receives and sends the information to be transmitted remotely prepared by the target receiving user for the target receiving user, and the non-target receiving user performs the base measurement operation, and sends the measurement result to the target receiving user user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements;
  • the target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
  • the present invention also provides a system for optional remote preparation of a two-bit state based on a cluster state terminal, including:
  • the sending user is used to remotely prepare the information to be transmitted for the target receiving user, construct a matrix based on the information to be transmitted and perform matrix operations and measurements, wherein direct entanglement can be formed between the sending user and the receiving user edge node channel;
  • a receiving user edge node where a GHZ channel can be formed between the receiving user edge node and the plurality of candidate receiving users
  • the plurality of candidate receiving users including target receiving users and non-target receiving users, wherein the non-target receiving users are used to perform base measurement operations and send the measurement results to the target receiving users, so
  • the target receiving user is used to perform matrix operations on the held particles, and perform unitary operations according to the measurement results of non-target receiving users to restore the information to be transmitted.
  • the present invention considers the situation that there are multiple candidate receiving users in the information transmission process.
  • the communication process is firstly divided into two steps: the sending user and the receiving user edge node construct a direct entanglement channel and the receiving user edge node constructs a GHZ channel with multiple candidate receiving users , and these two steps can be carried out at the same time, and the sending user determines the target receiving user while constructing the direct entanglement channel, and completes the terminal communication with the assistance of the non-target receiving user, which effectively reduces the communication delay, and considers that the channel bits are due to noise
  • the present invention can construct a matrix according to the dislocation information of each intermediate node to restore the information to be transmitted, which is more in line with the requirements of actual communication scenarios.
  • FIG. 1 is a schematic flowchart of a method for optionally remotely preparing a two-bit state based on a cluster state terminal in the present invention.
  • FIG. 2 is a schematic channel diagram of a method for remotely preparing a two-bit state based on a cluster state terminal in the present invention.
  • Fig. 3 is a comparison table of the phase detection result of the sending user and the unitary operation of the target receiving user in the present invention.
  • the CNOT operation is a NOT gate operation, and the two qubits are the control bit and the target bit respectively.
  • the control bit is
  • the matrix form of CNOT operation on qubit pairs is as follows:
  • the control phase gate which has two input qubits, is the control qubit and the target qubit. Its function is: when the control qubit and the target qubit are in
  • Embodiment 1 of the present invention A method for remotely preparing a two-bit state based on a cluster state terminal in Embodiment 1 of the present invention is described in detail below.
  • S100 Determine a direct entanglement channel between a sending user and a receiving user edge node, and simultaneously determine GHZ channels between the receiving user edge node and multiple candidate receiving users.
  • the system includes a sending user, a receiving user edge node and multiple candidate receiving users.
  • the maximum entanglement cluster state channel is used to connect between them.
  • determining the direct entanglement channel between the sending user and the receiving user edge node includes: there are multiple intermediate nodes between the sending user and the receiving user edge node, and the non-maximally entangled cluster state channel is used between the multiple intermediate nodes. Connection; the sending terminal and each intermediate node perform CZ operation on the held particles, and the intermediate node performs Bell measurement on the held particles, and sends the measurement result to the sending user, and the sending user determines its relationship with the receiving user according to the measurement result Direct entanglement channels between edge nodes. While the intermediate node sends the Bell measurement result to the sending user, the intermediate node sends the channel bit error information to the sending user, and the sending user determines the channel matrix that constitutes the direct quantum communication according to the measurement result and the channel bit error information.
  • determining the GHZ channel between the receiving user edge node and multiple candidate receiving users includes: the receiving user edge node performs CZ operation, CNOT operation and base measurement on the particles it holds, and sends the measurement results to the candidate receiving users, Candidate receiving users perform unitary operations on the particles they hold, and construct GHZ channels between receiving user edge nodes and multiple candidate receiving users.
  • S200 Determine the target receiving user among multiple candidate receiving users while constructing the direct entanglement channel, remotely prepare the information to be transmitted by the sending user as the target receiving user, perform the base measurement operation by the non-target receiving user, and send the measurement result to the target The receiving user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements.
  • the sending user constructs a matrix according to the information to be transmitted and performs matrix operation and measurement includes: constructing a matrix according to the information to be transmitted; using the matrix to perform matrix operations, and constructing a phase measurement base pair particle according to the phase information of the information to be transmitted Take measurements.
  • the target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
  • the target receiving user performs unitary operation according to the measurement result of the non-target receiving user, and restoring the information to be transmitted includes: if the measurement result of the particle by the non-target receiving user is
  • the present invention considers the situation that there are multiple candidate receiving users in the process of information transmission, and the communication process is firstly divided into the construction of a direct entanglement channel between the sending user and the edge node of the receiving user, and the construction of a GHZ channel between the edge node of the receiving user and multiple candidate receiving users Two steps, and these two steps can be carried out at the same time, and the sending user determines the target receiving user while constructing the direct entanglement channel, and completes the terminal communication with the assistance of the non-target receiving user, which effectively reduces the communication delay and considers the channel Bit errors may occur due to the influence of noise, etc.
  • the present invention can construct a matrix according to the bit error information of each intermediate node to restore the information to be transmitted, which is more in line with the needs of actual communication scenarios.
  • FIG. 1 and FIG. 2 the following describes in detail a method for remotely preparing a two-bit state based on a cluster state-based terminal in the form of an embodiment.
  • N+1 N>2 intermediate nodes between the sending user Alice and the candidate receiving user, and non-maximally entangled cluster state channels are used between the nodes.
  • N+1 N>2
  • the sending users Alice and Bob jointly prepare two bits of quantum state information remotely to the target receiving user Dave. Among them, Alice and Bob act as the sending user and hold part of the quantum state information to be prepared respectively, and Dave acts as the receiving user.
  • the sending user Alice and Bob help the target receiving user Dave to remotely prepare the target state as follows: Among them, ⁇ 0 , ⁇ 1 , ⁇ 2 , ⁇ 3 are known parameters and satisfy the normalization condition Among them, the sending user Alice holds amplitude information, and the sending user Bob holds phase information.
  • the receiving user edge node and the candidate receiving user are connected by a maximum entangled cluster state channel, where a 1 , a 2 ,...,an , b 1 ,b 2 ,...,b n belong to the receiving user edge node, c 1 ,c 2 ,...,c n , d 1 ,d 2 ,...,d n belong to candidate receiving users.
  • the receiving user edge node owns the particle a 1 , a 2 ,...,a n , b 1 ,b 2 ,...,b n .
  • the entire quantum system state is expressed as follows:
  • a method for remotely preparing a two-bit state based on a cluster state-based terminal may include the following:
  • Step 1 First, the receiving user edge node and 2n candidate receiving users are connected by the maximum entanglement cluster state channel, particles a 1 , a 2 ,...,a n , b 1 ,b 2 ,...,b n ,
  • the corrected state of c 1 ,c 2 ,...,c n , d 1 ,d 2 ,...,d n is:
  • Receive user edge node pairs of particles (a 1 ,a 2 ),(a 1 ,a 3 ),...,(a 1 ,a n ) and (b 1 ,b 2 ),(b 1 ,b 3 ),..., (b 1 , b n ) perform CNOT operation respectively, where a 1 and b 1 are control qubits, a 2 , a 3 ,...,a n and b 2 , b 3 ,...,b n are target qubits, the system state can be written as:
  • ⁇ x ⁇ is a 2 , a 3 ,..., a 0, 1 sequence of a n
  • ⁇ y ⁇ is a 0, 1 sequence of b 2 , b 3 ,..., b n ;
  • Indicates the negation of ⁇ x ⁇ Indicates the negation of ⁇ y ⁇ .
  • the edge node of the receiving user performs ⁇
  • the receiving user performs corresponding unitary operations on the particles c 2 , c 3 ,...,c n and d 2 , d 3 ,...,d n respectively to restore the GHZ channel.
  • the GHZ channel between the receiving user edge node and the candidate receiving user is as follows:
  • Step 2 The sending user Alice and the receiving user edge node are connected to each other by a non-maximally entangled cluster state channel, and the system state between the sending user Alice and the receiving user edge node can be expressed as:
  • the sending user Alice and each intermediate node first check the held particles To implement CZ operation, the system state can be written as:
  • the sending user Alice determines the channel matrix that constitutes direct quantum communication according to the measurement results and bit error information:
  • the sending user Alice can form a direct entanglement channel with the receiving user edge node according to the measurement results of each intermediate node.
  • the expression of the redefine coefficient is as follows:
  • step 1 and step 2 can be performed simultaneously, and the target receiving user among multiple candidate receiving users is determined while constructing the direct entanglement channel.
  • Step 3 In the above step 2, after the intermediate node performs the Bell measurement on the held particles, assuming that the candidate receiving user Dave is determined as the target receiving user, then the sending user Alice remotely prepares two bits to be transmitted for the target receiving user Dave Quantum state information.
  • the sending user Alice introduces the auxiliary particle
  • the remaining 2n-2 candidate receiving users perform H operation on the particles c 2 , c 3 ,...,c n , d 2 ,d 3 ,...,d n held by them.
  • the system state can be written as:
  • the measurement base is:
  • m 1 , n 1 , m 2 , and n 2 represent the measurement results of the Bell state.
  • symbol " ⁇ " and "-” represent XOR, AND and NOT operations, respectively.
  • the target receives user Dave to execute the matrix for particles c 1 and d 1 held by him
  • the target receiving user Dave can recover the target state. If the measurement results of non-target receiving users on particles c 2 , c 3 ,...,c n , d 2 ,d 3 ,...,d n are
  • the probability ⁇ of Alice helping the target receiving user to prepare the target state is:
  • the parameters of the direct entanglement channel formed by the edge nodes of the sending user and the receiving user can be determined to be
  • step 3 the information to be prepared can be obtained again as a participating channel through phase measurement.
  • two candidate receiving users and two intermediate nodes with undetermined terminals are taken as examples for illustration.
  • the sending user Alice helps the target receiving user Dave to prepare the target state as follows:
  • ⁇ 0 , ⁇ 1 , ⁇ 2 , ⁇ 3 are known parameters and satisfy the normalization condition
  • the receiving user edge node and the candidate receiving user are connected by a maximum entangled cluster state channel, where a 1 , a 2 , b 1 , b 2 belong to the receiving user edge node, c 1 , c 2 , d 1 , d 2 belong to Candidate receiving users.
  • the sending user Alice and the receiving user edge nodes are connected to each other by a non-maximally entangled cluster state channel, and Alice has particle
  • the intermediate node Charlie has particles
  • the receiving user edge node owns the particle a 1 , a 2 , b 1 , b 2 , the state of the entire quantum system is expressed as follows:
  • Step 1 The entanglement state between the receiving user edge node and the candidate receiving user is:
  • the receiving user edge node performs CZ operation on particles (a 1 , a 2 ) and (b 1 , b 2 ) respectively, and performs CNOT operation on (a 1 , a 2 ), (b 1 , b 2 ), the target node’s
  • the system state can be written as
  • ⁇ x ⁇ is the 0, 1 sequence of a 2
  • ⁇ y ⁇ is the 0, 1 sequence of b 2
  • Indicates the negation of ⁇ x ⁇ Indicates the negation of ⁇ y ⁇ .
  • the edge node of the receiving user performs ⁇
  • the receiving user performs corresponding unitary operations on particles c 2 and d 2 to restore the GHZ channel. If the measurement results of particles a 2 and b 2 by the receiving user edge node are both
  • the GHZ channel between the receiving user edge node and the candidate receiving user is as follows:
  • Step 2 The sending user Alice and the receiving user edge node are connected to each other by a non-maximally entangled cluster state channel, and the system state between the sending user Alice and the receiving user edge node can be expressed as:
  • the sending user Alice determines the channel matrix that constitutes direct quantum communication according to the measurement results and bit error information:
  • Step 3 In the above step 2, after performing the Bell measurement on the particles held by the intermediate node, assuming that the candidate receiving user Dave is determined as the target receiving user, the sending user Alice introduces the auxiliary particle
  • the direct entanglement channel between user edge nodes can be written as:
  • the remaining non-target candidate receiving users perform H operation on the particles c 2 and d 2 held by them, and the system state can be written as:
  • Alice constructs a matrix based on the information to be transmitted and acts on the system r particles, and construct a suitable phase measurement basis according to the phase information of the transmitted information, and For measurement, the system state can be written as:
  • the state related to the target state can be obtained as follows:
  • the target receiving user Dave can restore the target state according to the base measurement results of the particles c 2 and d 2 by the non-target receiving user. If the measurement results of non-target receiving users on particles c 2 , c 3 ,...,c n , d 2 ,d 3 ,...,d n are
  • Embodiment 2 of the present invention is an introduction to a system for remotely preparing a two-bit state based on a cluster state terminal that is provided by Embodiment 2 of the present invention.
  • a system for remotely preparing a two-bit state based on a cluster state terminal is described in the following
  • a method for remotely preparing two-bit states based on a cluster state based on a terminal optional remote preparation described in this paper can be referred to each other.
  • a system for optional remote preparation of two-bit states based on cluster state terminals including:
  • the sending user the sending user is used to remotely prepare the information to be transmitted for the target receiving user, construct a matrix according to the information to be transmitted, and perform matrix operation and measurement, wherein a direct entanglement channel can be formed between the sending user and the receiving user edge node;
  • the receiving user edge node can form a GHZ channel between the receiving user edge node and multiple candidate receiving users;
  • a plurality of candidate receiving users including target receiving users and non-target receiving users, wherein non-target receiving users are used to perform basement measurement operations and send measurement results to target receiving users, and target receiving users are used to Some particles perform matrix operations, and perform unitary operations based on the measurement results of non-target receiving users to restore the information to be transmitted.
  • a cluster state-based terminal optional remote preparation system for two-bit states in this embodiment is used to realize the aforementioned method for cluster state-based terminal optional remote preparation of two-bit states, so the specific implementation of the system
  • the method can be seen in the above-mentioned embodiment part of a method for remotely preparing two-bit states based on a cluster state terminal. Therefore, its specific implementation methods can refer to the descriptions of the corresponding embodiments of each part, and will not be introduced here. .
  • the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
  • computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions
  • the device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

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Abstract

The present invention relates to a cluster-state-based terminal-selectable method for remotely preparing a two-bit state. The method comprises: determining a direct entanglement channel between a sending user and a receiving user edge node, and determining a GHZ channel between the receiving user edge node and a plurality of candidate receiving users; determining a target receiving user from the plurality of candidate receiving users, remotely preparing, for the target receiving user, information to be transmitted, performing a substrate measurement operation by a non-target receiving user, and sending a measurement result to the target receiving user; and the target receiving user performing a matrix operation on possessed particles, and performing a unitary operation according to the measurement result of the non-target receiving user, so as to recover said information. According to the present invention, a target receiving user is determined while a direct entanglement channel is constructed, and terminal communications are completed with the help of an auxiliary operation of a non-target receiving user, thereby effectively reducing a communication delay; and information to be transmitted can be recovered by constructing a matrix according to dislocation information of each intermediate node, thereby meeting the requirement of an actual communication scenario to a greater extent.

Description

基于团簇态的终端可选远程制备两比特态的方法及***Method and system for optional remote preparation of two-bit states based on cluster states 技术领域technical field
本发明涉及光通信网络及信息传播技术领域，尤其是指一种基于团簇态的终端可选远程制备两比特态的方法及***。The invention relates to the technical field of optical communication network and information dissemination, in particular to a method and system for optionally remotely preparing two-bit states by terminals based on cluster states.
背景技术Background technique
近年来，众多学者热衷于对量子通信的研究，量子通信也逐渐由点对点的通信转向基于量子网路的通信。根据SECOQC(Development of a Global Network for Secure Communication based on Quantum Cryptography)组织的定义，量子通信网络是基于通信网络中节点与节点之间的量子密钥分配，使网络中的通信双方能够准确的交换理论上安全的密钥。量子通信网络中一般采用量子中继器作为网络中的中间节点，通过中间节点之间的纠缠信道相互连接可以构成链式信道，然后终端节点和网络中的中继节点对所持有的粒子分别实施Bell测量操作，最终使待传未知量子态在目的节点持有的粒子上“还原”出来，可以基于EPR协议最终可实现两个通信节点之间的通信。In recent years, many scholars are keen on the research of quantum communication, and quantum communication has gradually shifted from point-to-point communication to communication based on quantum network. According to the definition of SECOQC (Development of a Global Network for Secure Communication based on Quantum Cryptography), the quantum communication network is based on the quantum key distribution between nodes in the communication network, so that the communication parties in the network can exchange the theory accurately secure key. In the quantum communication network, quantum repeaters are generally used as the intermediate nodes in the network. Through the entanglement channels between the intermediate nodes, a chain channel can be formed, and then the particles held by the terminal nodes and the relay nodes in the network are divided into The Bell measurement operation is implemented, and finally the unknown quantum state to be transmitted is "restored" on the particles held by the destination node, and the communication between two communication nodes can be finally realized based on the EPR protocol.
随着双向量子态制备、控制量子态制备以及多方量子态远程制备等方案被提出，涌现出很多量子态远程制备方案。目前很多量子远程态制备通信方案均是基于发送用户和接收用户已定的条件下实现，缺少接收用户可选情形下的量子态远程制备方案。With the proposal of two-way quantum state preparation, controlled quantum state preparation, and remote preparation of multi-party quantum states, many quantum state remote preparation schemes have emerged. At present, many quantum remote state preparation communication schemes are realized based on the conditions of the sending user and the receiving user, and there is a lack of quantum state remote preparation schemes under the optional situation of the receiving user.
团簇态是一种新型多粒子纠缠态，相比较其他类型纠缠态，具有更强的稳定性和抗干扰性，而且同时具备GHZ态与W态的纠缠特性，近年来被广泛地应用到量子计算、量子安全直接通信(QSDC)和量子态远程制备等研究领 域。2016年提出了在理论上实现了四比特团簇态的远程制备，成功概率取决于量子信道纠缠态的系数。随后，2017年提出了基于n个最大纠缠两比特量子态实现了任意多比特态的制备，该方案利用迭代法详细描述了幺正操作的表达式，并分别计算了在一般情况和特殊情况下制备成功的概率。然后，2019年提出了任意四比特态的远程制备方案，该方案采用六比特团簇态作为通信信道，实现一个发送方、两个信息接收方之间的通信。上述提到的方案均是通信双方直接共享纠缠信道完成信息传输。然而实际的通信环境中，由于环境噪声等原因，信道比特可能发生位错而影响通信质量，因此很难符合实际通信场景的需求。Cluster state is a new type of multi-particle entangled state. Compared with other types of entangled states, it has stronger stability and anti-interference, and has the entanglement characteristics of GHZ state and W state at the same time. It has been widely used in quantum in recent years. Research fields such as computing, quantum secure direct communication (QSDC) and remote preparation of quantum states. In 2016, it was proposed to theoretically realize the remote preparation of four-bit cluster states, and the probability of success depends on the coefficient of the entangled state of the quantum channel. Subsequently, in 2017, it was proposed to realize the preparation of any multi-bit state based on n maximum entangled two-bit quantum states. This scheme described the expression of the unitary operation in detail by using the iterative method, and calculated the general and special cases respectively. Probability of preparation success. Then, in 2019, a remote preparation scheme for any four-bit state was proposed, which uses a six-bit cluster state as a communication channel to realize communication between one sender and two information receivers. In the above-mentioned schemes, the communication parties directly share the entanglement channel to complete the information transmission. However, in the actual communication environment, due to environmental noise and other reasons, the channel bits may be misplaced and affect the communication quality, so it is difficult to meet the needs of actual communication scenarios.
发明内容Contents of the invention
为此，本发明所要解决的技术问题在于克服现有技术中缺少接收用户可选情形下的量子通信方案以及因信道比特发生位错而影响通信质量使其不符合实际通信场景需求的缺陷。For this reason, the technical problem to be solved by the present invention is to overcome the defects in the prior art that there is no quantum communication scheme under the optional situation of the receiving user and that the communication quality is affected by the bit error of the channel bit so that it does not meet the requirements of the actual communication scene.
为解决上述技术问题，本发明提供了一种基于团簇态的终端可选远程制备两比特态的方法，所述***包括发送用户、接收用户边缘节点和多个候选接收用户，方法包括：In order to solve the above technical problems, the present invention provides a method for optional remote preparation of a two-bit state based on a terminal in a cluster state. The system includes a sending user, a receiving user edge node, and multiple candidate receiving users. The method includes:
确定发送用户与接收用户边缘节点之间的直接纠缠信道，同时确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道；determining a direct entanglement channel between a sending user and a receiving user edge node, and simultaneously determining GHZ channels between the receiving user edge node and a plurality of candidate receiving users;
在构建直接纠缠信道的同时确定多个候选接收用户中的目标接收用户，所述发送用户为所述目标接收用户远程制备待传送信息，由非目标接收用户进行基底测量操作，并将所述测量结果发送至所述目标接收用户，其中所述发送用户根据所述待传送信息构造矩阵并进行矩阵操作和测量；While constructing the direct entanglement channel, the target receiving user among multiple candidate receiving users is determined, the sending user remotely prepares the information to be transmitted for the target receiving user, and the base measurement operation is performed by the non-target receiving user, and the measured The result is sent to the target receiving user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements;
所述目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。The target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
在本发明的一个实施例中，确定发送用户与接收用户边缘节点之间的直接纠缠信道包括：In one embodiment of the present invention, determining the direct entanglement channel between the sending user and the receiving user edge node includes:
发送用户与接收用户边缘节点之间存在多个中间节点，多个中间节点之间均采用非最大纠缠团簇态信道进行连接；There are multiple intermediate nodes between the sending user and the receiving user's edge node, and the non-maximally entangled cluster state channels are used to connect between multiple intermediate nodes;
发送用户和各个中间节点各自对持有的粒子进行CZ操作，并由中间节点对持有的粒子执行Bell测量，并将测量结果发送至发送用户，所述发送用户根据测量结果确定其与接收用户边缘节点之间的直接纠缠信道。The sending user and each intermediate node perform CZ operation on the held particles respectively, and the intermediate node performs Bell measurement on the held particles, and sends the measurement result to the sending user, and the sending user determines its relationship with the receiving user according to the measurement result Direct entanglement channels between edge nodes.
在本发明的一个实施例中，在所述中间节点将Bell测量结果发送至发送用户的同时，所述中间节点将信道位错信息发送至发送用户，所述发送用户根据测量结果和信道位错信息确定构成直接量子通信的信道矩阵。In an embodiment of the present invention, when the intermediate node sends the Bell measurement result to the sending user, the intermediate node sends the channel bit error information to the sending user, and the sending user The information determines the channel matrix that constitutes direct quantum communication.
在本发明的一个实施例中，发送用户与接收用户边缘节点之间采用非最大纠缠团簇态信道进行连接。In one embodiment of the present invention, the non-maximally entangled cluster state channel is used for connection between the edge node of the sending user and the receiving user.
在本发明的一个实施例中，确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道包括：In an embodiment of the present invention, determining the GHZ channel between the receiving user edge node and multiple candidate receiving users includes:
所述接收用户边缘节点对持有的粒子进行CZ操作、CNOT操作和基底测量，并将测量结果发送给候选接收用户，所述候选接收用户对持有的粒子进行幺正操作，并在所述接收用户边缘节点与多个候选接收用户之间构建GHZ信道。The receiving user edge node performs CZ operation, CNOT operation and base measurement on the held particles, and sends the measurement results to the candidate receiving user, and the candidate receiving user performs unitary operation on the held particles, and A GHZ channel is constructed between the receiving user edge node and multiple candidate receiving users.
在本发明的一个实施例中，所述接收用户边缘节点与多个候选接收用户之间采用最大纠缠团簇态信道进行连接。In an embodiment of the present invention, the edge node of the receiving user is connected to multiple candidate receiving users using a maximum entangled cluster state channel.
在本发明的一个实施例中，所述目标接收用户根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息包括：In one embodiment of the present invention, the target receiving user performs a unitary operation according to the measurement results of the non-target receiving user, and restoring the information to be transmitted includes:
若非目标接收用户对粒子的测量结果是|{x}>|{y}>，那么目标接收用户能够 直接恢复待传送信息；若非目标接收用户对粒子的测量结果不是|{x}>|{y}>，那么目标接收用户需要对持有粒子执行Z操作来恢复待传送信息。If the measurement result of the particle by the non-target receiving user is |{x}>|{y}>, then the target receiving user can directly recover the information to be transmitted; if the measurement result of the non-target receiving user on the particle is not |{x}>|{y }>, then the target receiving user needs to perform the Z operation on the held particle to recover the information to be transmitted.
并且，本发明还提供一种由发送用户执行基于团簇态的终端可选远程制备两比特态的方法，包括：Moreover, the present invention also provides a method for the sending user to perform optional remote preparation of a two-bit state based on the terminal of the cluster state, including:
确定发送用户与接收用户边缘节点之间的直接纠缠信道；Determine the direct entanglement channel between the sending user and the receiving user edge node;
在构建直接纠缠信道的同时确定多个候选接收用户中的目标接收用户，为所述目标接收用户远程制备待传送信息，根据所述待传送信息构造矩阵并，进行矩阵操作和测量，其中非目标接收用户进行基底测量操作，并将所述测量结果发送至所述目标接收用户，所述目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。While constructing the direct entanglement channel, determine the target receiving user among multiple candidate receiving users, remotely prepare the information to be transmitted for the target receiving user, construct a matrix according to the information to be transmitted, and perform matrix operation and measurement, among which the non-target The receiving user performs base measurement operations, and sends the measurement results to the target receiving user, and the target receiving user performs matrix operations on the particles held, and performs unitary operations according to the measurement results of non-target receiving users, and restores Information to be sent.
此外，本发明还提供由候选接收用户执行基于团簇态的终端可选远程制备两比特态的方法，包括：In addition, the present invention also provides a method for candidate receiving users to perform terminal optional remote preparation of two-bit states based on cluster states, including:
确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道；determining GHZ channels between the receiving user edge node and multiple candidate receiving users;
在构建直接纠缠信道同时确定的目标接收用户接收发送用户为所述目标接收用户远程制备的待传送信息，并由非目标接收用户进行基底测量操作，并将所述测量结果发送至所述目标接收用户，其中所述发送用户根据所述待传送信息构造矩阵并进行矩阵操作和测量；The target receiving user determined while constructing the direct entanglement channel receives and sends the information to be transmitted remotely prepared by the target receiving user for the target receiving user, and the non-target receiving user performs the base measurement operation, and sends the measurement result to the target receiving user user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements;
所述目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。The target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
还有，本发明还提供一种基于团簇态的终端可选远程制备两比特态的***，包括：In addition, the present invention also provides a system for optional remote preparation of a two-bit state based on a cluster state terminal, including:
发送用户，所述发送用户用于为目标接收用户远程制备待传送信息，根 据所述待传送信息构造矩阵并进行矩阵操作和测量，其中所述发送用户与接收用户边缘节点之间可以形成直接纠缠信道；The sending user is used to remotely prepare the information to be transmitted for the target receiving user, construct a matrix based on the information to be transmitted and perform matrix operations and measurements, wherein direct entanglement can be formed between the sending user and the receiving user edge node channel;
接收用户边缘节点，所述接收用户边缘节点与所述多个候选接收用户之间可以形成GHZ信道；A receiving user edge node, where a GHZ channel can be formed between the receiving user edge node and the plurality of candidate receiving users;
多个候选接收用户，多个候选接收用户包括目标接收用户和非目标接收用户，其中所述非目标接收用户用于进行基底测量操作，并将所述测量结果发送至所述目标接收用户，所述目标接收用户用于对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。a plurality of candidate receiving users, the plurality of candidate receiving users including target receiving users and non-target receiving users, wherein the non-target receiving users are used to perform base measurement operations and send the measurement results to the target receiving users, so The target receiving user is used to perform matrix operations on the held particles, and perform unitary operations according to the measurement results of non-target receiving users to restore the information to be transmitted.
本发明的上述技术方案相比现有技术具有以下优点：The above technical solution of the present invention has the following advantages compared with the prior art:
本发明考虑在信息传输过程中存在多个候选接收用户的情形，通信过程首先分为发送用户与接收用户边缘节点构建直接纠缠信道以及接收用户边缘节点和多个候选接收用户构建GHZ信道两个步骤，并且这两个步骤可同时进行，并且发送用户在构建直接纠缠信道的同时确定目标接收用户，借助非目标接收用户辅助操作完成终端通信，有效减少了通信时延，而且考虑到信道比特由于噪声等影响可能发生位错的原因，本发明可根据各中间节点的位错信息构造矩阵来恢复待传送信息，更符合实际通信场景的需求。The present invention considers the situation that there are multiple candidate receiving users in the information transmission process. The communication process is firstly divided into two steps: the sending user and the receiving user edge node construct a direct entanglement channel and the receiving user edge node constructs a GHZ channel with multiple candidate receiving users , and these two steps can be carried out at the same time, and the sending user determines the target receiving user while constructing the direct entanglement channel, and completes the terminal communication with the assistance of the non-target receiving user, which effectively reduces the communication delay, and considers that the channel bits are due to noise The present invention can construct a matrix according to the dislocation information of each intermediate node to restore the information to be transmitted, which is more in line with the requirements of actual communication scenarios.
附图说明Description of drawings
为了使本发明的内容更容易被清楚的理解，下面根据本发明的具体实施例并结合附图，对本发明作进一步详细的说明。In order to make the content of the present invention more clearly understood, the present invention will be further described in detail below according to the specific embodiments of the present invention and in conjunction with the accompanying drawings.
图1是本发明基于团簇态的终端可选远程制备两比特态的方法的流程示意图。FIG. 1 is a schematic flowchart of a method for optionally remotely preparing a two-bit state based on a cluster state terminal in the present invention.
图2是本发明基于团簇态的终端可选远程制备两比特态的方法的信道示意图。FIG. 2 is a schematic channel diagram of a method for remotely preparing a two-bit state based on a cluster state terminal in the present invention.
图3是本发明发送用户的相位检测结果与目标接收用户幺正操作的对 照表。Fig. 3 is a comparison table of the phase detection result of the sending user and the unitary operation of the target receiving user in the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.
在介绍本发明内容之前，首先对本申请涉及到的技术名词进行说明，具体包括：Before introducing the content of the present invention, the technical terms involved in this application are first described, specifically including:
1、Pauli阵1. Pauli array
本发明中还会用到一些幺正矩阵，也即Pauli阵。具体形式如下：Some unitary matrices, ie Pauli matrices, will also be used in the present invention. The specific form is as follows:
Figure PCTCN2021143112-appb-000001
Figure PCTCN2021143112-appb-000001
Figure PCTCN2021143112-appb-000002
Figure PCTCN2021143112-appb-000002
Figure PCTCN2021143112-appb-000003
Figure PCTCN2021143112-appb-000003
Figure PCTCN2021143112-appb-000004
Figure PCTCN2021143112-appb-000004
2、CNOT操作2. CNOT operation
CNOT操作即为非门操作，两个量子比特分别为控制比特和目标比特。当控制比特是|0>时，目标比特不变；当控制比特是|1>时，目标比特发生反转。CNOT操作对量子比特对作用的矩阵形式如下：The CNOT operation is a NOT gate operation, and the two qubits are the control bit and the target bit respectively. When the control bit is |0>, the target bit remains unchanged; when the control bit is |1>, the target bit is inverted. The matrix form of CNOT operation on qubit pairs is as follows:
Figure PCTCN2021143112-appb-000005
Figure PCTCN2021143112-appb-000005
3、控制相位门3. Control phase gate
控制相位门(CZ门)，它拥有两个输入量子比特，分别是控制量子比特和目标量子比特。其作用是：当控制量子比特与目标量子比特同时处于|1>时，将这两个体态的相位反转π。其对应的矩阵形式为：The control phase gate (CZ gate), which has two input qubits, is the control qubit and the target qubit. Its function is: when the control qubit and the target qubit are in |1> at the same time, the phases of the two states are reversed by π. Its corresponding matrix form is:
Figure PCTCN2021143112-appb-000006
Figure PCTCN2021143112-appb-000006
实施例一Embodiment one
下面对本发明实施例一提供的一种基于团簇态的终端可选远程制备两比特态的方法进行详细的阐述。A method for remotely preparing a two-bit state based on a cluster state terminal in Embodiment 1 of the present invention is described in detail below.
请参阅图1和图2所示，一种基于团簇态的终端可选远程制备两比特态的方法，包括如下步骤：Please refer to Figure 1 and Figure 2, a method for remotely preparing a two-bit state based on a cluster state-based terminal, including the following steps:
S100、确定发送用户与接收用户边缘节点之间的直接纠缠信道，同时确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道。S100. Determine a direct entanglement channel between a sending user and a receiving user edge node, and simultaneously determine GHZ channels between the receiving user edge node and multiple candidate receiving users.
示例地，***包括发送用户、接收用户边缘节点和多个候选接收用户，发送用户与接收用户边缘节点之间采用非最大纠缠团簇态信道进行连接，接收用户边缘节点与多个候选接收用户之间采用最大纠缠团簇态信道进行连接。Exemplarily, the system includes a sending user, a receiving user edge node and multiple candidate receiving users. The maximum entanglement cluster state channel is used to connect between them.
示例地，确定发送用户与接收用户边缘节点之间的直接纠缠信道包括：发送用户与接收用户边缘节点之间存在多个中间节点，多个中间节点之间均采用非最大纠缠团簇态信道进行连接；送终端和各个中间节点各自对持有的粒子进行CZ操作，并由中间节点对持有的粒子执行Bell测量，并将测量结果发送至发送用户，发送用户根据测量结果确定其与接收用户边缘节点之间的直接纠缠信道。在中间节点将Bell测量结果发送至发送用户的同时，中间节点将信道位错信息发送至发送用户，发送用户根据测量结果和信道位错信 息确定构成直接量子通信的信道矩阵。Exemplarily, determining the direct entanglement channel between the sending user and the receiving user edge node includes: there are multiple intermediate nodes between the sending user and the receiving user edge node, and the non-maximally entangled cluster state channel is used between the multiple intermediate nodes. Connection; the sending terminal and each intermediate node perform CZ operation on the held particles, and the intermediate node performs Bell measurement on the held particles, and sends the measurement result to the sending user, and the sending user determines its relationship with the receiving user according to the measurement result Direct entanglement channels between edge nodes. While the intermediate node sends the Bell measurement result to the sending user, the intermediate node sends the channel bit error information to the sending user, and the sending user determines the channel matrix that constitutes the direct quantum communication according to the measurement result and the channel bit error information.
示例地，确定接收用户边缘节点与多个候选接收用户之间的GHZ信道包括：接收用户边缘节点对持有的粒子进行CZ操作、CNOT操作和基底测量，并将测量结果发送给候选接收用户，候选接收用户对持有的粒子进行幺正操作，并在接收用户边缘节点与多个候选接收用户之间构建GHZ信道。Exemplarily, determining the GHZ channel between the receiving user edge node and multiple candidate receiving users includes: the receiving user edge node performs CZ operation, CNOT operation and base measurement on the particles it holds, and sends the measurement results to the candidate receiving users, Candidate receiving users perform unitary operations on the particles they hold, and construct GHZ channels between receiving user edge nodes and multiple candidate receiving users.
S200、在构建直接纠缠信道的同时确定多个候选接收用户中的目标接收用户，发送用户为目标接收用户远程制备待传送信息，由非目标接收用户进行基底测量操作，并将测量结果发送至目标接收用户，其中发送用户根据所述待传送信息构造矩阵并进行矩阵操作和测量。S200. Determine the target receiving user among multiple candidate receiving users while constructing the direct entanglement channel, remotely prepare the information to be transmitted by the sending user as the target receiving user, perform the base measurement operation by the non-target receiving user, and send the measurement result to the target The receiving user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements.
示例地，所述发送用户根据所述待传送信息构造矩阵并进行矩阵操作和测量包括：根据待传送信息构造矩阵；利用矩阵进行矩阵操作，并根据待传送信息的相位信息构建相位测量基对粒子进行测量。Exemplarily, the sending user constructs a matrix according to the information to be transmitted and performs matrix operation and measurement includes: constructing a matrix according to the information to be transmitted; using the matrix to perform matrix operations, and constructing a phase measurement base pair particle according to the phase information of the information to be transmitted Take measurements.
S300、目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。S300. The target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
示例地，目标接收用户根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息包括：若非目标接收用户对粒子的测量结果是|{x}>|{y}>，那么目标接收用户能够直接恢复待传送信息；若非目标接收用户对粒子的测量结果不是|{x}>|{y}>，那么目标接收用户需要对持有粒子执行Z操作来恢复待传送信息。For example, the target receiving user performs unitary operation according to the measurement result of the non-target receiving user, and restoring the information to be transmitted includes: if the measurement result of the particle by the non-target receiving user is |{x}>|{y}>, then the target receiving user Can directly restore the information to be transmitted; if the measurement result of the particle by the non-target receiving user is not |{x}>|{y}>, then the target receiving user needs to perform the Z operation on the held particle to restore the information to be transmitted.
综上，本发明考虑在信息传输过程中存在多个候选接收用户的情形，通信过程首先分为发送用户与接收用户边缘节点构建直接纠缠信道以及接收用户边缘节点和多个候选接收用户构建GHZ信道两个步骤，并且这两个步骤可同时进行，并且发送用户在构建直接纠缠信道的同时确定目标接收用户，借 助非目标接收用户辅助操作完成终端通信，有效减少了通信时延，而且考虑到信道比特由于噪声等影响可能发生位错的原因，本发明可根据各中间节点的位错信息构造矩阵来恢复待传送信息，更符合实际通信场景的需求。In summary, the present invention considers the situation that there are multiple candidate receiving users in the process of information transmission, and the communication process is firstly divided into the construction of a direct entanglement channel between the sending user and the edge node of the receiving user, and the construction of a GHZ channel between the edge node of the receiving user and multiple candidate receiving users Two steps, and these two steps can be carried out at the same time, and the sending user determines the target receiving user while constructing the direct entanglement channel, and completes the terminal communication with the assistance of the non-target receiving user, which effectively reduces the communication delay and considers the channel Bit errors may occur due to the influence of noise, etc. The present invention can construct a matrix according to the bit error information of each intermediate node to restore the information to be transmitted, which is more in line with the needs of actual communication scenarios.
请继续参阅图1和图2所示，下面以实施例的方式详细介绍本发明一种基于团簇态的终端可选远程制备两比特态的方法。Please continue to refer to FIG. 1 and FIG. 2 , the following describes in detail a method for remotely preparing a two-bit state based on a cluster state-based terminal in the form of an embodiment.
在该实施例中，发送用户Alice和候选接收用户之间存在N+1(N>2)个中间节点，且节点之间均采用非最大纠缠团簇态信道，在确定候选接收用户Dave为目标接收用户时，发送用户Alice和Bob联合给目标接收用户Dave远程制备两比特量子态信息。其中，Alice和Bob一起作为发送用户，并分别持有部分待制备量子态信息，Dave作为接收用户。In this embodiment, there are N+1 (N>2) intermediate nodes between the sending user Alice and the candidate receiving user, and non-maximally entangled cluster state channels are used between the nodes. When determining the candidate receiving user Dave as the target When receiving users, the sending users Alice and Bob jointly prepare two bits of quantum state information remotely to the target receiving user Dave. Among them, Alice and Bob act as the sending user and hold part of the quantum state information to be prepared respectively, and Dave acts as the receiving user.
传送过程中发送用户Alice和Bob帮助目标接收用户Dave远程制备目标态为：
Figure PCTCN2021143112-appb-000007
其中λ 0,λ 1,λ 2,λ 3为已知参数，且满足归一化条件
Figure PCTCN2021143112-appb-000008
其中，发送用户Alice持有幅度信息，发送用户Bob持有相位信息。 During the transmission process, the sending user Alice and Bob help the target receiving user Dave to remotely prepare the target state as follows:
Figure PCTCN2021143112-appb-000007
Among them, λ 0 , λ 1 , λ 2 , λ 3 are known parameters and satisfy the normalization condition
Figure PCTCN2021143112-appb-000008
Among them, the sending user Alice holds amplitude information, and the sending user Bob holds phase information.
接收用户边缘节点与候选接收用户之间由最大纠缠团簇态信道相互连接，其中a 1,a 2,…,a n、b 1,b 2,…,b n属于接收用户边缘节点，c 1,c 2,…,c n、d 1,d 2,…,d n属于候选接收用户。发送用户Alice和接收用户边缘节点之间由非最大纠缠团簇态信道相互连接，其中发送用户Alice拥有粒子
Figure PCTCN2021143112-appb-000009
中间节点Charlie i(i＝1,2,…,N+1)拥有粒子
Figure PCTCN2021143112-appb-000010
接收用户边缘节点拥有粒子
Figure PCTCN2021143112-appb-000011
a 1,a 2,…,a n、b 1,b 2,…,b n。整个量子***态表示如下： The receiving user edge node and the candidate receiving user are connected by a maximum entangled cluster state channel, where a 1 , a 2 ,…,an , b 1 ,b 2 ,…,b n belong to the receiving user edge node, c 1 ,c 2 ,...,c n , d 1 ,d 2 ,...,d n belong to candidate receiving users. The sending user Alice and the receiving user edge nodes are connected to each other by a non-maximally entangled cluster state channel, in which the sending user Alice has particle
Figure PCTCN2021143112-appb-000009
Intermediate node Charlie i (i=1,2,…,N+1) owns particles
Figure PCTCN2021143112-appb-000010
The receiving user edge node owns the particle
Figure PCTCN2021143112-appb-000011
a 1 , a 2 ,…,a n , b 1 ,b 2 ,…,b n . The entire quantum system state is expressed as follows:
Figure PCTCN2021143112-appb-000012
Figure PCTCN2021143112-appb-000012
具体的，一种基于团簇态的终端可选远程制备两比特态的方法包括如下内容：Specifically, a method for remotely preparing a two-bit state based on a cluster state-based terminal may include the following:
步骤一：首先，接收用户边缘节点与2n个候选接收用户之间由最大纠缠团簇态信道相互连接，粒子a 1,a 2,…,a n、b 1,b 2,…,b n、c 1,c 2,…,c n、d 1,d 2,…,d n的纠态为： Step 1: First, the receiving user edge node and 2n candidate receiving users are connected by the maximum entanglement cluster state channel, particles a 1 , a 2 ,…,a n , b 1 ,b 2 ,…,b n , The corrected state of c 1 ,c 2 ,…,c n , d 1 ,d 2 ,…,d n is:
Figure PCTCN2021143112-appb-000013
Figure PCTCN2021143112-appb-000013
接收用户边缘节点对粒子(a 2i-1,a 2i)、(b 2i-1,b 2i)(i＝1,2,…,n/2)分别实施CZ操作，其中a 2i-1、b 2i-1为控制量子比特，a 2i、b 2i为目标量子比特，***态可以写为： The receiving user edge node implements CZ operation on particles (a 2i-1 , a 2i ), (b 2i-1 , b 2i ) (i=1,2,…,n/2) respectively, where a 2i-1 , b 2i-1 is the control qubit, a 2i and b 2i are the target qubits, the system state can be written as:
Figure PCTCN2021143112-appb-000014
Figure PCTCN2021143112-appb-000014
接收用户边缘节点对粒子(a 1,a 2),(a 1,a 3),…,(a 1,a n)和(b 1,b 2),(b 1,b 3),…,(b 1,b n)分别进行CNOT操作，其中a 1和b 1是控制量子比特，a 2,a 3,…,a n和b 2,b 3,…,b n为目标量子比特，***态可以写为： Receive user edge node pairs of particles (a 1 ,a 2 ),(a 1 ,a 3 ),…,(a 1 ,a n ) and (b 1 ,b 2 ),(b 1 ,b 3 ),…, (b 1 , b n ) perform CNOT operation respectively, where a 1 and b 1 are control qubits, a 2 , a 3 ,...,a n and b 2 , b 3 ,...,b n are target qubits, the system state can be written as:
Figure PCTCN2021143112-appb-000015
Figure PCTCN2021143112-appb-000015
其中，{x}是a 2,a 3,…,a n的0，1序列，{y}是b 2,b 3,…,b n的0，1序列；
Figure PCTCN2021143112-appb-000016
表示对{x}取反，
Figure PCTCN2021143112-appb-000017
表示对{y}取反。 Among them, {x} is a 2 , a 3 ,…, a 0, 1 sequence of a n , {y} is a 0, 1 sequence of b 2 , b 3 ,…, b n ;
Figure PCTCN2021143112-appb-000016
Indicates the negation of {x},
Figure PCTCN2021143112-appb-000017
Indicates the negation of {y}.
接收用户边缘节点再分别对粒子a 2,a 3,…,a n和b 2,b 3,…,b n执行{|0>,|1>}基底测量，并将测量结果发送给接收用户。接收用户分别对粒子c 2,c 3,…,c n和d 2,d 3,…,d n执行相应幺正操作，恢复出GHZ信道。接收用户边缘节点和候选接收用户之间构成GHZ信道如下： The edge node of the receiving user performs {|0>,|1>} basis measurement on particles a 2 , a 3 ,…,a n and b 2 ,b 3 ,…,b n respectively, and sends the measurement results to the receiving user . The receiving user performs corresponding unitary operations on the particles c 2 , c 3 ,...,c n and d 2 , d 3 ,...,d n respectively to restore the GHZ channel. The GHZ channel between the receiving user edge node and the candidate receiving user is as follows:
Figure PCTCN2021143112-appb-000018
Figure PCTCN2021143112-appb-000018
步骤二：发送用户Alice和接收用户边缘节点之间由非最大纠缠团簇态信道相互连接，发送用户Alice和接收用户边缘节点之间***态可表示为：Step 2: The sending user Alice and the receiving user edge node are connected to each other by a non-maximally entangled cluster state channel, and the system state between the sending user Alice and the receiving user edge node can be expressed as:
Figure PCTCN2021143112-appb-000019
Figure PCTCN2021143112-appb-000019
发送用户Alice与各中间节点先对持有的粒子
Figure PCTCN2021143112-appb-000020
实施CZ操作，***态可以写为： The sending user Alice and each intermediate node first check the held particles
Figure PCTCN2021143112-appb-000020
To implement CZ operation, the system state can be written as:
Figure PCTCN2021143112-appb-000021
Figure PCTCN2021143112-appb-000021
上式的***态可以写为：The system state of the above formula can be written as:
Figure PCTCN2021143112-appb-000022
Figure PCTCN2021143112-appb-000022
中间节点Charlie i(i＝1,2,…,N)对所拥有的粒子
Figure PCTCN2021143112-appb-000023
和
Figure PCTCN2021143112-appb-000024
分别以|φ 00>,|φ 01>,|φ 10>,|φ 11>为测量基实施Bell态测量，并将测量结果发送给Alice，发送用户Alice根据测量结果即可确定其与接收用户之间的直接纠缠信道
Figure PCTCN2021143112-appb-000025
其中
Figure PCTCN2021143112-appb-000026
中u,v和s,t均为0，1组合。 The particles owned by the intermediate node Charlie i (i=1,2,…,N)
Figure PCTCN2021143112-appb-000023
and
Figure PCTCN2021143112-appb-000024
Take |φ 00 >, |φ 01 >, |φ 10 >, |φ 11 > as the measurement basis to implement the Bell state measurement respectively, and send the measurement results to Alice. direct entanglement channel
Figure PCTCN2021143112-appb-000025
in
Figure PCTCN2021143112-appb-000026
Among them, u, v and s, t are all 0, 1 combination.
经过中间节点Charlie i公布Bell测量结果和位错信息之后，发送用户Alice根据测量结果和位错信息，确定构成直接量子通信的信道矩阵为： After the intermediate node Charlie i publishes the Bell measurement results and bit error information, the sending user Alice determines the channel matrix that constitutes direct quantum communication according to the measurement results and bit error information:
Figure PCTCN2021143112-appb-000027
Figure PCTCN2021143112-appb-000027
发送用户Alice根据各中间节点的测量结果可与接收用户边缘节点构成直接纠缠信道。为了便于分析，重新定义系数的表示方式如下：The sending user Alice can form a direct entanglement channel with the receiving user edge node according to the measurement results of each intermediate node. In order to facilitate the analysis, the expression of the redefine coefficient is as follows:
Figure PCTCN2021143112-appb-000028
Figure PCTCN2021143112-appb-000028
Figure PCTCN2021143112-appb-000029
Figure PCTCN2021143112-appb-000029
值得说明的是，上述步骤一和步骤二可以同时进行，而且在构建直接纠缠信道的同时确定多个候选接收用户中的目标接收用户。It is worth noting that the above step 1 and step 2 can be performed simultaneously, and the target receiving user among multiple candidate receiving users is determined while constructing the direct entanglement channel.
步骤三：在上述步骤二中，中间节点在对所持有的粒子执行Bell测量之后，假设确定候选接收用户Dave为目标接收用户，那么发送用户Alice为目标接收用户Dave远程制备待传送的两比特量子态信息。发送用户Alice引入辅助粒子|0> r，发送用户Alice与接收用户边缘节点之间的直接纠缠信道可写为： Step 3: In the above step 2, after the intermediate node performs the Bell measurement on the held particles, assuming that the candidate receiving user Dave is determined as the target receiving user, then the sending user Alice remotely prepares two bits to be transmitted for the target receiving user Dave Quantum state information. The sending user Alice introduces the auxiliary particle |0> r , and the direct entanglement channel between the sending user Alice and the receiving user edge node can be written as:
Figure PCTCN2021143112-appb-000030
Figure PCTCN2021143112-appb-000030
其余2n-2个候选接收用户对各自持有的粒子c 2,c 3,…,c n，d 2,d 3,…,d n进行H操作，***态可以写为： The remaining 2n-2 candidate receiving users perform H operation on the particles c 2 , c 3 ,…,c n , d 2 ,d 3 ,…,d n held by them. The system state can be written as:
Figure PCTCN2021143112-appb-000031
Figure PCTCN2021143112-appb-000031
发送用户Alice设定
Figure PCTCN2021143112-appb-000032
且
Figure PCTCN2021143112-appb-000033
Alice根据待传送信息构造矩阵如下： Send user Alice settings
Figure PCTCN2021143112-appb-000032
and
Figure PCTCN2021143112-appb-000033
Alice constructs a matrix according to the information to be transmitted as follows:
Figure PCTCN2021143112-appb-000034
Figure PCTCN2021143112-appb-000034
其中in
Figure PCTCN2021143112-appb-000035
Figure PCTCN2021143112-appb-000035
在构造矩阵时若待传送信息λ i(i＝0,1,2,3)等于0时，对应的子矩阵
Figure PCTCN2021143112-appb-000036
When constructing the matrix, if the information to be transmitted λ i (i=0,1,2,3) is equal to 0, the corresponding sub-matrix
Figure PCTCN2021143112-appb-000036
发送用户将矩阵
Figure PCTCN2021143112-appb-000037
作用于***中
Figure PCTCN2021143112-appb-000038
r粒子上，
Figure PCTCN2021143112-appb-000039
的***态可以写为： Sending user will matrix
Figure PCTCN2021143112-appb-000037
acting on the system
Figure PCTCN2021143112-appb-000038
on the r particle,
Figure PCTCN2021143112-appb-000039
The system state of can be written as:
Figure PCTCN2021143112-appb-000040
Figure PCTCN2021143112-appb-000040
并根据待传送信息的相位信息构建合适的相位测量基{|μ jk>；j,k∈{0,1}}对粒子对
Figure PCTCN2021143112-appb-000041
执行测量。测量基为： And according to the phase information of the information to be transmitted, construct a suitable phase measurement basis {|μ jk >; j,k∈{0,1}} pair of particles
Figure PCTCN2021143112-appb-000041
Perform measurements. The measurement base is:
Figure PCTCN2021143112-appb-000042
Figure PCTCN2021143112-appb-000042
Figure PCTCN2021143112-appb-000043
Figure PCTCN2021143112-appb-000043
Figure PCTCN2021143112-appb-000044
Figure PCTCN2021143112-appb-000044
Figure PCTCN2021143112-appb-000045
Figure PCTCN2021143112-appb-000045
Figure PCTCN2021143112-appb-000046
的***态可以写为：
Figure PCTCN2021143112-appb-000046
The system state of can be written as:
Figure PCTCN2021143112-appb-000047
Figure PCTCN2021143112-appb-000047
其中|{x}>、|{y}>为二进制{|0>,|1>}序列，且含有偶数个1；
Figure PCTCN2021143112-appb-000048
含有奇数个1。 Where |{x}>, |{y}> are binary {|0>,|1>} sequences, and contain an even number of 1s;
Figure PCTCN2021143112-appb-000048
Contains an odd number of 1s.
矩阵
Figure PCTCN2021143112-appb-000049
的矩阵形式为： matrix
Figure PCTCN2021143112-appb-000049
The matrix form of is:
Figure PCTCN2021143112-appb-000050
Figure PCTCN2021143112-appb-000050
Figure PCTCN2021143112-appb-000051
Figure PCTCN2021143112-appb-000051
其中in
Figure PCTCN2021143112-appb-000052
Figure PCTCN2021143112-appb-000052
Figure PCTCN2021143112-appb-000053
Figure PCTCN2021143112-appb-000053
Figure PCTCN2021143112-appb-000054
Figure PCTCN2021143112-appb-000054
Figure PCTCN2021143112-appb-000055
Figure PCTCN2021143112-appb-000055
上式中，m 1,n 1,m 2,n 2表示Bell态的测量结果。符号
Figure PCTCN2021143112-appb-000056
“·”和“-”分别代表异或、与和非操作。 In the above formula, m 1 , n 1 , m 2 , and n 2 represent the measurement results of the Bell state. symbol
Figure PCTCN2021143112-appb-000056
"·" and "-" represent XOR, AND and NOT operations, respectively.
忽略全局相位，目标接收用户Dave对其持有的粒子c 1、d 1执行矩阵
Figure PCTCN2021143112-appb-000057
Figure PCTCN2021143112-appb-000058
的矩阵操作和图3中与发送用户投影测量对应的幺正操作，当Alice对粒子r测量结果为|0> r，可获得与目标态相关的态： Ignoring the global phase, the target receives user Dave to execute the matrix for particles c 1 and d 1 held by him
Figure PCTCN2021143112-appb-000057
Figure PCTCN2021143112-appb-000058
The matrix operation of and the unitary operation corresponding to the projection measurement of the sending user in Figure 3, when Alice’s measurement result of particle r is |0> r , the state related to the target state can be obtained:
Figure PCTCN2021143112-appb-000059
Figure PCTCN2021143112-appb-000059
目标接收用户Dave根据非目标接收用户对粒子c 2,c 3,…,c n、d 2,d 3,…,d n的{|0>,|1>}基底测量结果，可恢复出目标态。若非目标接收用户对粒子c 2,c 3,…,c n、d 2,d 3,…,d n的测量结果为|{x}>|{y}>，目标接收用户Dave可以直接获得目标态；若测量结果为
Figure PCTCN2021143112-appb-000060
目标接收用户Dave需要对持有粒子d 1执行Z操作，可恢复出目标态；若测量结果为
Figure PCTCN2021143112-appb-000061
目标接收用户Dave需要对持有粒子c 1执行Z操作；若测量结果为
Figure PCTCN2021143112-appb-000062
目标接收用户Dave需要对持有的粒子执行c 1和d 1都执行Z操作，可恢复出目标态。 The target receiving user Dave can recover the target state. If the measurement results of non-target receiving users on particles c 2 , c 3 ,…,c n , d 2 ,d 3 ,…,d n are |{x}>|{y}>, the target receiving user Dave can directly obtain the target state; if the measurement result is
Figure PCTCN2021143112-appb-000060
The target receiving user Dave needs to perform the Z operation on the holding particle d 1 to restore the target state; if the measurement result is
Figure PCTCN2021143112-appb-000061
The target receiving user Dave needs to perform the Z operation on the holding particle c 1 ; if the measurement result is
Figure PCTCN2021143112-appb-000062
The target receiving user Dave needs to perform the Z operation on both c 1 and d 1 to restore the target state.
当发送用户Alice对粒子r测量结果为|0> r，Alice帮助目标接收用户制备出目标态成功的概率η为： When the sending user Alice measures the particle r with |0> r , the probability η of Alice helping the target receiving user to prepare the target state is:
Figure PCTCN2021143112-appb-000063
Figure PCTCN2021143112-appb-000063
当Alice对粒子r的测量结果为|1> r时，即可确定发送用户与接收用户边缘节点构成的直接纠缠信道的参数分别为
Figure PCTCN2021143112-appb-000064
Figure PCTCN2021143112-appb-000065
When Alice’s measurement result of particle r is |1> r , the parameters of the direct entanglement channel formed by the edge nodes of the sending user and the receiving user can be determined to be
Figure PCTCN2021143112-appb-000064
Figure PCTCN2021143112-appb-000065
发送用户可以令Sending user can order
Figure PCTCN2021143112-appb-000066
然后按照步骤三中的方法继续设定
Figure PCTCN2021143112-appb-000067
且
Figure PCTCN2021143112-appb-000068
采用相似的递归操作可以重新作为参与信道通过相位测量获得待制备信息。
Figure PCTCN2021143112-appb-000066
Then follow the method in step 3 to continue setting
Figure PCTCN2021143112-appb-000067
and
Figure PCTCN2021143112-appb-000068
Using a similar recursive operation, the information to be prepared can be obtained again as a participating channel through phase measurement.
下面以终端未定的2个候选接收用户和2个中间节点为例进行举例说明。In the following, two candidate receiving users and two intermediate nodes with undetermined terminals are taken as examples for illustration.
传送过程中发送用户Alice帮助目标接收用户Dave制备目标态为：During the transmission process, the sending user Alice helps the target receiving user Dave to prepare the target state as follows:
Figure PCTCN2021143112-appb-000069
其中λ 0,λ 1,λ 2,λ 3为已知参数，且满足归一化条件
Figure PCTCN2021143112-appb-000070
Figure PCTCN2021143112-appb-000069
Among them, λ 0 , λ 1 , λ 2 , λ 3 are known parameters and satisfy the normalization condition
Figure PCTCN2021143112-appb-000070
接收用户边缘节点与候选接收用户之间由最大纠缠团簇态信道相互连接，其中a 1,a 2,b 1,b 2属于接收用户边缘节点，c 1,c 2,d 1,d 2属于候选接收用户。发送用户Alice和接收用户边缘节点之间由非最大纠缠团簇态信道相互连接，Alice拥有粒子
Figure PCTCN2021143112-appb-000071
中间节点Charlie拥有粒子
Figure PCTCN2021143112-appb-000072
接收用户边缘节点拥有粒子
Figure PCTCN2021143112-appb-000073
a 1,a 2,b 1,b 2，整个量子***态表示如下： The receiving user edge node and the candidate receiving user are connected by a maximum entangled cluster state channel, where a 1 , a 2 , b 1 , b 2 belong to the receiving user edge node, c 1 , c 2 , d 1 , d 2 belong to Candidate receiving users. The sending user Alice and the receiving user edge nodes are connected to each other by a non-maximally entangled cluster state channel, and Alice has particle
Figure PCTCN2021143112-appb-000071
The intermediate node Charlie has particles
Figure PCTCN2021143112-appb-000072
The receiving user edge node owns the particle
Figure PCTCN2021143112-appb-000073
a 1 , a 2 , b 1 , b 2 , the state of the entire quantum system is expressed as follows:
Figure PCTCN2021143112-appb-000074
Figure PCTCN2021143112-appb-000074
步骤一：接收用户边缘节点与候选接收用户之间的纠缠态为：Step 1: The entanglement state between the receiving user edge node and the candidate receiving user is:
Figure PCTCN2021143112-appb-000075
Figure PCTCN2021143112-appb-000075
接收用户边缘节点对粒子(a 1,a 2)、(b 1,b 2)分别实施CZ操作，并对(a 1,a 2),(b 1,b 2)进行CNOT操作，目标节点的***态可以写为 The receiving user edge node performs CZ operation on particles (a 1 , a 2 ) and (b 1 , b 2 ) respectively, and performs CNOT operation on (a 1 , a 2 ), (b 1 , b 2 ), the target node’s The system state can be written as
Figure PCTCN2021143112-appb-000076
Figure PCTCN2021143112-appb-000076
其中，{x}是a 2的0，1序列，{y}是b 2的0，1序列；
Figure PCTCN2021143112-appb-000077
表示对{x}取反，
Figure PCTCN2021143112-appb-000078
表示对{y}取反。 Among them, {x} is the 0, 1 sequence of a 2 , and {y} is the 0, 1 sequence of b 2 ;
Figure PCTCN2021143112-appb-000077
Indicates the negation of {x},
Figure PCTCN2021143112-appb-000078
Indicates the negation of {y}.
接收用户边缘节点再分别对粒子a 2和b 2执行{|0>,|1>}基底测量，并将测量结果发送给接收用户。接收用户分别对粒子c 2和d 2执行相应幺正操作，恢复出GHZ信道。如果接收用户边缘节点对粒子a 2和b 2的测量结果都为|1>，则接收用户对相应粒子c 2和d 2执行X操作；若接收用户边缘节点对粒子a 2和b 2的测量结果都为|0>，测接收用户对相应粒子c 2和d 2执行I操作。接收用户边缘节点和候选接收用户之间构成GHZ信道如下： The edge node of the receiving user performs {|0>,|1>} basis measurement on particles a 2 and b 2 respectively, and sends the measurement results to the receiving user. The receiving user performs corresponding unitary operations on particles c 2 and d 2 to restore the GHZ channel. If the measurement results of particles a 2 and b 2 by the receiving user edge node are both | 1 >, then the receiving user performs X operation on the corresponding particles c 2 and d 2 ; The results are all |0>, and the receiving user performs the I operation on the corresponding particles c 2 and d 2 . The GHZ channel between the receiving user edge node and the candidate receiving user is as follows:
Figure PCTCN2021143112-appb-000079
Figure PCTCN2021143112-appb-000079
步骤二：发送用户Alice和接收用户边缘节点之间由非最大纠缠团簇态信道相互连接，发送用户Alice和接收用户边缘节点之间***态可表示为：Step 2: The sending user Alice and the receiving user edge node are connected to each other by a non-maximally entangled cluster state channel, and the system state between the sending user Alice and the receiving user edge node can be expressed as:
Figure PCTCN2021143112-appb-000080
Figure PCTCN2021143112-appb-000080
发送用户Alice与2个中间节点先对粒子
Figure PCTCN2021143112-appb-000081
实施CZ操作，***态可以写为： Send user Alice and 2 intermediate nodes to first pair particles
Figure PCTCN2021143112-appb-000081
To implement CZ operation, the system state can be written as:
Figure PCTCN2021143112-appb-000082
Figure PCTCN2021143112-appb-000082
经过中间节点公布Bell测量结果和位错信息后，发送用户Alice根据测量结果和位错信息，确定构成直接量子通信的信道矩阵为：After the intermediate node publishes the Bell measurement results and bit error information, the sending user Alice determines the channel matrix that constitutes direct quantum communication according to the measurement results and bit error information:
Figure PCTCN2021143112-appb-000083
Figure PCTCN2021143112-appb-000083
步骤三：在上述步骤二中，中间节点在对所持有的粒子执行Bell测量之后，假设确定候选接收用户Dave为目标接收用户，发送用户Alice引入辅助粒子|0> r，发送用户Alice与接收用户边缘节点之间的直接纠缠信道可写为： Step 3: In the above step 2, after performing the Bell measurement on the particles held by the intermediate node, assuming that the candidate receiving user Dave is determined as the target receiving user, the sending user Alice introduces the auxiliary particle |0> r , and the sending user Alice and the receiving user The direct entanglement channel between user edge nodes can be written as:
Figure PCTCN2021143112-appb-000084
Figure PCTCN2021143112-appb-000084
其余的非目标候选接收用户对持有的粒子c 2，d 2进行H操作，***态可以写为： The remaining non-target candidate receiving users perform H operation on the particles c 2 and d 2 held by them, and the system state can be written as:
Figure PCTCN2021143112-appb-000085
Figure PCTCN2021143112-appb-000085
Alice根据待传送信息构造矩阵并作用于***中
Figure PCTCN2021143112-appb-000086
r粒子上，并根据传送信息的相位信息构建合适的相位测量基并对
Figure PCTCN2021143112-appb-000087
进测量，***态可以写为： Alice constructs a matrix based on the information to be transmitted and acts on the system
Figure PCTCN2021143112-appb-000086
r particles, and construct a suitable phase measurement basis according to the phase information of the transmitted information, and
Figure PCTCN2021143112-appb-000087
For measurement, the system state can be written as:
Figure PCTCN2021143112-appb-000088
Figure PCTCN2021143112-appb-000088
其中|{x}>、|{y}>为二进制{|0>,|1>}序列，且含有偶数个1；
Figure PCTCN2021143112-appb-000089
含有奇数个1。 Where |{x}>, |{y}> are binary {|0>,|1>} sequences, and contain an even number of 1s;
Figure PCTCN2021143112-appb-000089
Contains an odd number of 1s.
当Alice对粒子r测量结果为|0> r，可获得与目标态相关的态如下： When Alice measures the particle r as |0> r , the state related to the target state can be obtained as follows:
Figure PCTCN2021143112-appb-000090
Figure PCTCN2021143112-appb-000090
目标接收用户Dave根据非目标接收用户对粒子c 2，d 2的基底测量结果，可恢复出目标态。若非目标接收用户对粒子c 2,c 3,…,c n、d 2,d 3,…,d n的测量结果为|{x}>|{y}>，目标接收用户Dave可以直接获得目标态；若测量结果为
Figure PCTCN2021143112-appb-000091
目标接收用户Dave需要对持有粒子d 1执行Z操作，可恢复出目标 态；若测量结果为
Figure PCTCN2021143112-appb-000092
目标接收用户Dave需要对持有粒子c 1执行Z操作；若测量结果为
Figure PCTCN2021143112-appb-000093
目标接收用户Dave需要对持有的粒子执行c 1和d 1都执行Z操作，可恢复出目标态。 The target receiving user Dave can restore the target state according to the base measurement results of the particles c 2 and d 2 by the non-target receiving user. If the measurement results of non-target receiving users on particles c 2 , c 3 ,…,c n , d 2 ,d 3 ,…,d n are |{x}>|{y}>, the target receiving user Dave can directly obtain the target state; if the measurement result is
Figure PCTCN2021143112-appb-000091
The target receiving user Dave needs to perform the Z operation on the holding particle d 1 to restore the target state; if the measurement result is
Figure PCTCN2021143112-appb-000092
The target receiving user Dave needs to perform the Z operation on the holding particle c 1 ; if the measurement result is
Figure PCTCN2021143112-appb-000093
The target receiving user Dave needs to perform the Z operation on both c 1 and d 1 to restore the target state.
实施例二Embodiment two
下面对本发明实施例二提供的一种基于团簇态的终端可选远程制备两比特态的***进行介绍，下文描述的一种基于团簇态的终端可选远程制备两比特态的***与上文描述的一种基于团簇态的终端可选远程制备两比特态的方法可相互对应参照。The following is an introduction to a system for remotely preparing a two-bit state based on a cluster state terminal that is provided by Embodiment 2 of the present invention. A system for remotely preparing a two-bit state based on a cluster state terminal is described in the following A method for remotely preparing two-bit states based on a cluster state based on a terminal optional remote preparation described in this paper can be referred to each other.
一种基于团簇态的终端可选远程制备两比特态的***，包括：A system for optional remote preparation of two-bit states based on cluster state terminals, including:
发送用户，发送用户用于为目标接收用户远程制备待传送信息，根据待传送信息构造矩阵并进行矩阵操作和测量，其中发送用户与接收用户边缘节点之间可以形成直接纠缠信道；The sending user, the sending user is used to remotely prepare the information to be transmitted for the target receiving user, construct a matrix according to the information to be transmitted, and perform matrix operation and measurement, wherein a direct entanglement channel can be formed between the sending user and the receiving user edge node;
接收用户边缘节点，接收用户边缘节点与多个候选接收用户之间可以形成GHZ信道；The receiving user edge node can form a GHZ channel between the receiving user edge node and multiple candidate receiving users;
多个候选接收用户，多个候选接收用户包括目标接收用户和非目标接收用户，其中非目标接收用户用于进行基底测量操作，并将测量结果发送至目标接收用户，目标接收用户用于对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。A plurality of candidate receiving users, including target receiving users and non-target receiving users, wherein non-target receiving users are used to perform basement measurement operations and send measurement results to target receiving users, and target receiving users are used to Some particles perform matrix operations, and perform unitary operations based on the measurement results of non-target receiving users to restore the information to be transmitted.
本实施例的一种基于团簇态的终端可选远程制备两比特态的***用于实现前述的一种基于团簇态的终端可选远程制备两比特态的方法，因此该***的具体实施方式可见前文中的一种基于团簇态的终端可选远程制备两比特态的方法的实施例部分，所以，其具体实施方式可以参照相应的各个部分实施例的描述，在此不再展开介绍。A cluster state-based terminal optional remote preparation system for two-bit states in this embodiment is used to realize the aforementioned method for cluster state-based terminal optional remote preparation of two-bit states, so the specific implementation of the system The method can be seen in the above-mentioned embodiment part of a method for remotely preparing two-bit states based on a cluster state terminal. Therefore, its specific implementation methods can refer to the descriptions of the corresponding embodiments of each part, and will not be introduced here. .
另外，由于本实施例的一种基于团簇态的终端可选远程制备两比特态的***用于实现前述的一种基于团簇态的终端可选远程制备两比特态的方法，因此其作用与上述方法的作用相对应，这里不再赘述。In addition, since the system of a cluster state-based terminal optional remote preparation of two-bit states in this embodiment is used to realize the aforementioned method for cluster state-based terminal optional remote preparation of two-bit states, its function Corresponding to the effect of the above method, it will not be repeated here.
本领域内的技术人员应明白，本申请的实施例可提供为方法、***、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。Those skilled in the art should understand that the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
本申请是参照根据本申请实施例的方法、设备(***)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present application is described with reference to flowcharts and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.
显然，上述实施例仅仅是为清楚地说明所作的举例，并非对实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引申出的显而易见的变化或变动仍处于本发明创造的保护范围之中。Apparently, the above-mentioned embodiments are only examples for clear description, and are not intended to limit the implementation. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in various forms can also be made. It is not necessary and impossible to exhaustively list all the implementation manners here. However, the obvious changes or changes derived therefrom are still within the scope of protection of the present invention.

Claims (10)

  1. 一种基于团簇态的终端可选远程制备两比特态的方法，其特征在于，所述***包括发送用户、接收用户边缘节点和多个候选接收用户，方法包括：A method for remotely preparing a two-bit state based on a cluster state terminal, characterized in that the system includes a sending user, a receiving user edge node and a plurality of candidate receiving users, and the method includes:
    确定发送用户与接收用户边缘节点之间的直接纠缠信道，同时确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道；determining a direct entanglement channel between a sending user and a receiving user edge node, and simultaneously determining GHZ channels between the receiving user edge node and a plurality of candidate receiving users;
    在构建直接纠缠信道的同时确定多个候选接收用户中的目标接收用户，所述发送用户为所述目标接收用户远程制备待传送信息，由非目标接收用户进行基底测量操作，并将所述测量结果发送至所述目标接收用户，其中所述发送用户根据所述待传送信息构造矩阵并进行矩阵操作和测量；While constructing the direct entanglement channel, the target receiving user among multiple candidate receiving users is determined, the sending user remotely prepares the information to be transmitted for the target receiving user, and the base measurement operation is performed by the non-target receiving user, and the measured The result is sent to the target receiving user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements;
    所述目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。The target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
  2. 根据权利要求1所述的基于团簇态的终端可选远程制备两比特态的方法，其特征在于：确定发送用户与接收用户边缘节点之间的直接纠缠信道包括：The method for remotely preparing a two-bit state based on a cluster state terminal according to claim 1, wherein determining the direct entanglement channel between the sending user and the receiving user edge node comprises:
    发送用户与接收用户边缘节点之间存在多个中间节点，多个中间节点之间均采用非最大纠缠团簇态信道进行连接；There are multiple intermediate nodes between the sending user and the receiving user's edge node, and the non-maximally entangled cluster state channels are used to connect between multiple intermediate nodes;
    发送用户和各个中间节点各自对持有的粒子进行CZ操作，并由中间节点对持有的粒子执行Bell测量，并将测量结果发送至发送用户，所述发送用户根据测量结果确定其与接收用户边缘节点之间的直接纠缠信道。The sending user and each intermediate node perform CZ operation on the held particles respectively, and the intermediate node performs Bell measurement on the held particles, and sends the measurement result to the sending user, and the sending user determines its relationship with the receiving user according to the measurement result Direct entanglement channels between edge nodes.
  3. 根据权利要求2所述的基于团簇态的终端可选远程制备两比特态的方法，其特征在于：在所述中间节点将Bell测量结果发送至发送用户的同时，所述中间节点将信道位错信息发送至发送用户，所述发送用户根据测量结果和 信道位错信息确定构成直接量子通信的信道矩阵。The method for remotely preparing a two-bit state based on a cluster state terminal according to claim 2 is characterized in that: when the intermediate node sends the Bell measurement result to the sending user, the intermediate node sends the channel bit The error information is sent to the sending user, and the sending user determines the channel matrix constituting the direct quantum communication according to the measurement result and the channel bit error information.
  4. 根据权利要求1或2所述的基于团簇态的终端可选远程制备两比特态的方法，其特征在于：发送用户与接收用户边缘节点之间采用非最大纠缠团簇态信道进行连接。According to claim 1 or 2, the method for optional remote preparation of a two-bit state by a terminal based on a cluster state is characterized in that: the edge nodes of the sending user and the receiving user are connected using a non-maximally entangled cluster state channel.
  5. 根据权利要求1所述的基于团簇态的终端可选远程制备两比特态的方法，其特征在于：确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道包括：The method for optionally remotely preparing two-bit states based on cluster state terminals according to claim 1, wherein determining the GHZ channel between the receiving user edge node and multiple candidate receiving users comprises:
    所述接收用户边缘节点对持有的粒子进行CZ操作、CNOT操作和基底测量，并将测量结果发送给候选接收用户，所述候选接收用户对持有的粒子进行幺正操作，在所述接收用户边缘节点与多个候选接收用户之间构建GHZ信道。The edge node of the receiving user performs CZ operation, CNOT operation and base measurement on the particles it holds, and sends the measurement result to the candidate receiving user, and the candidate receiving user performs unitary operation on the particles it holds, GHZ channels are constructed between user edge nodes and multiple candidate receiving users.
  6. 根据权利要求1或5所述的基于团簇态的终端可选远程制备两比特态的方法，其特征在于：所述接收用户边缘节点与多个候选接收用户之间采用最大纠缠团簇态信道进行连接。According to claim 1 or 5, the method for remotely preparing a two-bit state based on a cluster state terminal is characterized in that: the maximum entanglement cluster state channel is used between the receiving user edge node and multiple candidate receiving users to connect.
  7. 根据权利要求1所述的基于团簇态的终端可选远程制备两比特态的方法方法，其特征在于：所述目标接收用户根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息包括：The method for remotely preparing a two-bit state based on a cluster state terminal according to claim 1, characterized in that: the target receiving user performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted include:
    若非目标接收用户对粒子的测量结果是|{x}>|{y}>，那么目标接收用户能够直接恢复待传送信息；若非目标接收用户对粒子的测量结果不是|{x}>|{y}>，那么目标接收用户需要对持有粒子执行Z操作来恢复待传送信息。If the measurement result of the particle by the non-target receiving user is |{x}>|{y}>, then the target receiving user can directly recover the information to be transmitted; if the measurement result of the non-target receiving user on the particle is not |{x}>|{y }>, then the target receiving user needs to perform the Z operation on the held particle to recover the information to be transmitted.
  8. 一种由发送用户执行基于团簇态的终端可选远程制备两比特态的方法，其特征在于，包括：A method for a sending user to perform optional remote preparation of a two-bit state based on a cluster state terminal, characterized in that it includes:
    确定发送用户与接收用户边缘节点之间的直接纠缠信道；Determine the direct entanglement channel between the sending user and the receiving user edge node;
    在构建直接纠缠信道的同时确定多个候选接收用户中的目标接收用户，为所述目标接收用户远程制备待传送信息，根据所述待传送信息构造矩阵并进行矩阵操作和测量，其中非目标接收用户进行基底测量操作，并将所述测量结果发送至所述目标接收用户，所述目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。While constructing the direct entanglement channel, determine the target receiving user among multiple candidate receiving users, remotely prepare the information to be transmitted for the target receiving user, construct a matrix according to the information to be transmitted, and perform matrix operation and measurement, wherein the non-target receiving user The user performs the base measurement operation, and sends the measurement result to the target receiving user, and the target receiving user performs a matrix operation on the held particles, and performs unitary operations according to the measurement results of the non-target receiving user, and restores the pending send information.
  9. 一种由候选接收用户执行基于团簇态的终端可选远程制备两比特态的方法，其特征在于，包括：A method for a candidate receiving user to perform optional remote preparation of a two-bit state based on a cluster state terminal, characterized in that it includes:
    确定所述接收用户边缘节点与多个候选接收用户之间的GHZ信道；determining GHZ channels between the receiving user edge node and multiple candidate receiving users;
    在构建直接纠缠信道同时确定的目标接收用户接收发送用户为所述目标接收用户远程制备的待传送信息，并由非目标接收用户进行基底测量操作，并将所述测量结果发送至所述目标接收用户，其中所述发送用户根据所述待传送信息构造矩阵并进行矩阵操作和测量；The target receiving user determined while constructing the direct entanglement channel receives and sends the information to be transmitted remotely prepared by the target receiving user for the target receiving user, and the non-target receiving user performs the base measurement operation, and sends the measurement result to the target receiving user user, wherein the sending user constructs a matrix according to the information to be transmitted and performs matrix operations and measurements;
    所述目标接收用户对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。The target receiving user performs a matrix operation on the held particles, and performs a unitary operation according to the measurement results of the non-target receiving user to restore the information to be transmitted.
  10. 一种基于团簇态的终端可选远程制备两比特态的***，其特征在于，包括：A system for optional remote preparation of a two-bit state based on a cluster state terminal, characterized in that it includes:
    发送用户，所述发送用户用于为目标接收用户远程制备待传送信息，根据所述待传送信息构造矩阵并进行矩阵操作和测量，其中所述发送用户与接收用户边缘节点之间形成直接纠缠信道；The sending user is used to remotely prepare information to be transmitted for the target receiving user, construct a matrix based on the information to be transmitted and perform matrix operations and measurements, wherein a direct entanglement channel is formed between the sending user and the edge node of the receiving user ;
    接收用户边缘节点，所述接收用户边缘节点与所述多个候选接收用户之间形成GHZ信道；a receiving user edge node, forming a GHZ channel between the receiving user edge node and the plurality of candidate receiving users;
    多个候选接收用户，多个候选接收用户包括目标接收用户和非目标接收用户，其中所述非目标接收用户用于进行基底测量操作，并将所述测量结果 发送至所述目标接收用户，所述目标接收用户用于对持有的粒子执行矩阵操作，并根据非目标接收用户的测量结果进行幺正操作，恢复待传送信息。a plurality of candidate receiving users, the plurality of candidate receiving users including target receiving users and non-target receiving users, wherein the non-target receiving users are used to perform base measurement operations and send the measurement results to the target receiving users, so The target receiving user is used to perform matrix operations on the held particles, and perform unitary operations according to the measurement results of non-target receiving users to restore the information to be transmitted.
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