CN114598396A - High-dimensional asymmetric bidirectional controlled quantum invisible state transfer method - Google Patents
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Abstract
The invention discloses a high-dimensional asymmetric bidirectional controlled quantum invisible state transfer method, which comprises the following steps: step 1, establishing a quantum communication combination system based on Alice, Bob and Charlie; step 2, respectively carrying out generalized Bell measurement and generalized single particle measurement on the particles owned by Alice and Bob, and publishing the measurement results; step 3, the supervisor Charlie carries out single particle measurement on the particles owned by the supervisor Charlie and publishes the measurement result; and 4, constructing the full appearance of the original quantum state transmitted by the opposite party by using the measurement result by the Alice and the Bob. The invention can realize the bidirectional transmission of quantum information; the success probability of the transmission and reduction of the quantum information is 1, the difficulty of specific communication control is greatly reduced, and the bidirectional controlled invisible transmission state is easier to physically realize.
Description
Technical Field
The invention relates to the technical field of quantum communication, in particular to a high-dimensional asymmetric bidirectional controlled quantum invisible state transfer method.
Background
With the progress of the times, people pay more attention to information safety. Quantum informatics is a novel interdiscipline generated by the combination of quantum mechanics and information science, and mainly comprises quantum computation and quantum communication. Since the rise of the eighties of the twentieth century, research related to quantum communication has been vigorously developed. Quantum communication has attracted attention because of its many advantages, such as ensuring information security, improving communication accuracy, and increasing storage capacity, compared with conventional communication methods. After more than thirty years of research, quantum communication has extended the research directions of quantum secure communication, quantum invisible transmission, quantum dense coding and the like, promotes the development of modern information science, and has wide development prospect.
Quantum entanglement is an important characteristic of quantum mechanics, and is widely applied to a plurality of research directions of quantum communication. Quantum entanglement refers to the interaction between particles in a composite system of two or more particles, and the state of one particle is influenced by the behavior of another particle even if the separation distance is large. In the early days of quantum communication development, studies on quantum entanglement have mostly focused on low-dimensional quantum systems, whereas in physics, high-dimensional spaces exist in addition to low-dimensional spaces. The research on the high-dimensional quantum entangled state has a certain theoretical value, and compared with the two-dimensional quantum entangled state, the high-dimensional quantum entangled state has the advantage of larger information carrying capacity and has more advantages in the aspects of improving the safety of a quantum communication scheme and processing quantum information.
Quantum invisible transport is a special way to transport unknown quantum states using quantum entanglement and classical communication. In 2001, zhou jing dong et al proposed a scheme for transporting unknown high-dimensional single-particle states, after which the study of invisible transport schemes for transporting high-dimensional unknown quantum states has attracted interest to numerous scholars. Studies on experiments relating to quantum communication have been actively conducted by researchers, but these experiments are limited to a low-dimensional space. Until 2019, the Panjianwei team in the Chinese academy of sciences realizes the three-dimensional quantum invisible transmission state for the first time, which shows that the research on high-dimensional quantum communication is applied from theory for the first time, and lays a foundation for the complete state transmission of a complex quantum system. Therefore, the current quantum invisible states mainly refer to quantum invisible states in a low-dimensional space.
In the article entitled "controllable quantum bidirectional invisible transmission state and security based on four-particle GHZ state", published by the report on photonics 2014, Hu, et al, a controllable quantum bidirectional transmission state scheme is provided for realizing unknown single-particle state based on four-particle GHZ entangled state, two communication parties Alice and Bob and a control party share two pairs of four-particle GHZ entangled states in advance to construct a quantum channel, the controllable quantum bidirectional transmission states participated by three parties and four parties can be respectively realized according to different distribution modes of entangled particles and different measurement bases selected during measurement, after communication begins, Alice and Bob respectively perform quantum projection measurement on part of particles owned by themselves, if the control party agrees to the communication between the two parties, the measurement is performed on the particles owned by themselves and the measurement results are published through a classical channel, the two communication parties perform corresponding per-unit correction transformation on a certain particle according to the measurement results published by the control party, but in the scheme, a channel is constructed in a four-particle GHZ state to transmit two-dimensional quantum states, the borne quantum information is less, and the safety of the quantum communication scheme needs to be improved.
In the study on a seven-particle entangled state bidirectional asymmetric control communication scheme published in 'Quantum electronics journal' in 2018, a seven-particle quantum entangled state bidirectional asymmetric control communication scheme serving as a quantum channel is proposed, in the scheme, Alic transmits any single qubit (or any two qubits) to Bob and Bob transmits any two qubits (or any two qubits) to Alice, and is controlled by a supervisor Charlie. However, in the scheme, a two-dimensional seven-particle state is used as a quantum channel, so that bidirectional asymmetric control is realized, the information carried by the particle state is less, and the security of the quantum communication scheme needs to be improved.
In summary, in the prior art, the bidirectional controlled quantum invisible state is mainly assumed to occur in a low-dimensional space, and in addition, researchers often assume that the numbers of particles to be transmitted of two communicating parties are equal, but in the discussion of practical problems, the numbers of particles to be transmitted of two communicating parties may be different, so that the assumption is contrary to the practice.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for high-dimensional asymmetric bidirectional controlled quantum invisible state transfer.
The purpose of the invention is realized by the following technical scheme:
a method for high-dimensional asymmetric bidirectional controlled quantum stealth states comprises the following steps:
step 1, establishing a quantum communication combination system based on Alice, Bob and Charlie: establishing a sender and a receiver of Alice and Bob in a high-dimensional single particle state and a high-dimensional two-particle state mutually, wherein Charlie is a monitor, two high-dimensional entangled states are used as quantum channels, and the Alice, the Bob and the Charlie share a quantum communication combined system of the two high-dimensional entangled states;
step 2, respectively carrying out generalized Bell measurement and generalized single particle measurement on the particles owned by Alice and Bob, and publishing the measurement results: in a quantum communication combined system, Alice and Bob form a particle pair by two shared high-dimensional entangled-state particles and a particle of an unknown particle state to be sent, correspondingly measure the particles, and publish the measurement results of the Alice and the Bob through a classical channel;
step 3, the supervisor Charlie carries out single particle measurement on the particles owned by the supervisor Charlie and publishes the measurement result: according to the measurement result of Alice and the measurement result of Bob, the supervisor Charlie respectively carries out single particle measurement on the owned particles and transmits the measurement result to Alice and Bob through a classical channel;
and 4, constructing the full appearance of the original quantum state transmitted by the opposite party by using the measurement result by the Alice and the Bob: and (3) by using the measurement results of the Alice and the Bob and combining the Charlie single-particle measurement result of the supervisor, separating the collapse state of the particle complex consisting of two high-dimensional particle states after measurement into a product state of two high-dimensional entangled state quantum information shared by the Alice and the Bob, and reconstructing the original state of the other party through unitary transformation.
Further, the two high-dimensional entangled states in step 1 are used as quantum channels, and the two high-dimensional entangled states of the quantum channels shared by Alice, Bob and Charlie adopt the maximum entangled state.
Further, in the step 1, Alice and Bob are both parties of quantum communication, and Alice and Bob are a sender and a receiver of unknown high-dimensional single particle state and high-dimensional two particle state, Alice serves as the sender to send the quantum state to Bob serving as the receiver, and Alice also serves as the receiver to receive the quantum state sent by Bob; charlie is a supervision party of quantum communication, under the control of Charlie, Alice reconstructs the quantum state transmitted by Bob, and Bob reconstructs the quantum state transmitted by Alice; particles in two high-dimensional entangled states, which are quantum channels, are assigned to Alice, Bob, and Charlie.
Further, the Alice and Bob in the step 4 construct the overall view of the original quantum state sent by the other party by using the measurement result, and Alice and Bob construct unitary transformation by using the measurement result of the Alice and the measurement result of the other party and combining the monitoring party Charlie single-particle measurement result, perform single-particle measurement on the auxiliary particle, separate the collapse state of the particle complex formed by two high-dimensional particle states after all measurements into the product state of two high-dimensional entangled-state quantum information shared by Alice and Bob, and reconstruct the original state of the other party by unitary transformation.
Further, the constructing unitary transform specifically includes: alice performs a unitary transform on the measured collapsed state of the particle complexes with a high-dimensional unitary transform matrix with respect to Alice possessing high-dimensional entangled-state particles, and Bob performs a unitary transform on the measured collapsed state of the particle complexes with respect to Bob possessing high-dimensional entangled-state particles with a high-dimensional unitary transform matrix.
Further, the reconstructing the original state of the other party by the unitary transformation specifically includes: and respectively applying unitary operation to the owned particles by Alice and Bob so as to realize the reconstruction of the original state of the particles.
The invention has the beneficial effects that: 1. according to the high-dimensional asymmetric bidirectional controlled quantum invisible state transfer method, two high-dimensional entangled states are used as quantum channels shared by Alice, Bob and a supervisor Charlie, so that bidirectional transfer of quantum information is realized; because Alice and Bob are a sender and a receiver, Alice performs generalized Bell measurement on the owned high-dimensional entangled-state particles and the particles to be sent, Bob performs generalized Bell measurement and generalized single particle measurement on the owned high-dimensional entangled-state particles and the particles to be sent, publishes the measurement result through a classical channel, and respectively transmits a high-dimensional two-particle state and a high-dimensional single particle state to the other side, thereby realizing the bidirectional transmission of quantum information, obviously, the quantum information carried in the communication process is far more than the quantum information carried by any particle, therefore, under the condition of the same information transmission efficiency, the invention has a much larger information amount than that transferred in the prior art in the same time; the monitor Charlie carries out single particle measurement on the high-dimensional entangled-state particles on the basis of the measurement results of Alice and Bob, and transmits the measurement results to Alice and Bob through a classical channel, so that help is provided for reconstruction of quantum states to be transmitted; the method is characterized in that Alice and Bob reduce the quantum collapse state into the product state of original quantum information by combining the self measurement result and the result of single particle measurement performed by the supervisor Charlie, so that the original state is reconstructed, namely the bidirectional reduction of the quantum information is realized under the control of the supervisor Charlie. The success probability of the transmission and reduction of the quantum information is 1.
2. The high-dimensional asymmetric bidirectional controlled quantum invisible state transfer method only adopts generalized Bell measurement and generalized single particle measurement, thereby greatly reducing the difficulty of specific communication control, enabling the bidirectional controlled invisible state transfer to be easier to physically realize, and taking the transfer of a three-dimensional particle state as an example, the method can be popularized to any d (d is more than or equal to 3) dimensional space.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a quantum communication combination system of Alice, Bob and Charlie.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In this embodiment, as shown in fig. 1, a high-dimensional asymmetric bidirectional controlled quantum invisible state transfer method includes four steps of establishing a quantum communication combination system based on three parties, namely Alice, Bob and Charlie, where Alice performs generalized Bell measurement on an owned high-dimensional entangled-state particle and a particle to be sent, Bob performs generalized Bell measurement and generalized single-particle measurement on an owned high-dimensional entangled-state particle and a particle to be sent, a measurement result is published through a classical channel, a supervisor Charlie performs single-particle measurement on an owned particle and publishes the measurement result, and Alice and Bob construct an overall view of an original quantum state sent by the other party by using the measurement result, which are specifically as follows:
step 1, establishing a quantum communication combination system based on Alice, Bob and Charlie: and establishing a quantum communication combined system in which Alice and Bob are mutually a sender and a receiver of high-dimensional particle states, Charlie is a monitor, two high-dimensional entangled states are used as quantum channels, and Alice, Bob and Charlie share two high-order entangled state particles.
As shown in fig. 2, Alice and Bob are both parties of quantum communication, and Alice and Bob are a sender and a receiver of unknown high-dimensional single-particle state and high-dimensional two-particle state, that is, Alice serves as the sender to send a quantum state to Bob serving as the receiver, and Alice also serves as the receiver to receive the quantum state sent by Bob; charlie is a supervision party of quantum communication, namely under the control of Charlie, Alice reconstructs the quantum state transmitted by Bob, and Bob reconstructs the quantum state transmitted by Alice; particles in two high-dimensional entangled states as quantum channels are allocated to three parties Alice, Bob, Charlie.
During implementation, according to actual needs of quantum communication, the two high-dimensional entangled-state particles are distributed to three parties including Alice, Bob and Charlie, the two high-order entangled states are used as quantum channels, the high-dimensional entangled state is the maximum entangled state, and a quantum communication combination system based on the three parties including Alice, Bob and Charlie is constructed by combining the unknown particle states to be sent by Alice and Bob.
Assuming that one three-particle maximally entangled state possesses three particles 1, 2, 3 and another four-particle entangled cluster state possesses four particles 4, 5, 6, 7 as quantum channels, taking a three-dimensional particle state as an example, the expressions of the two maximally entangled states:
it is assumed that Alice is assigned to a, 1, 5, 7 four particles, Bob is assigned to B, B', 3, 4 four particles, Charlie is assigned to 2, 6 two particles.
The unknown high-dimensional single particle to be transmitted to Bob by Alice under the control of a supervisor Charlie is A, and the particle state expression of the unknown high-dimensional single particle is as follows:
wherein | ψ 〉AIs a state relating to a single particle A, α0，α1，α2Is a state probability amplitude, α0，α1，α2Is plural and satisfies
；
Here and in the following, probability amplitudes, i.e. quantum amplitudes in quantum mechanics, are used to describe the quantum behavior of a particle.
Under the control of Charlie, a supervisor of Bob prepares to deliver unknown high-dimensional two-particles to Alice as B, B', and the particle state expression of the two-particle is as follows:
wherein | ψ 〉BB' is a state relating to a single particle A, β0，β1，β2Is a state probability amplitude, beta0，β1，β2Is plural and satisfies
；
Here and in the following, probability amplitude, i.e. quantum amplitude in quantum mechanics, is used to describe the quantum behavior of a particle.
Then, based on the two high-dimensional entangled states being quantum channels, Alice and Bob mutually send an unknown high-dimensional single particle state and a high-dimensional two-particle state to each other, and the quantum communication joint system with Charlie as a supervising party is as follows:
。
step 2, Alice and Bob respectively carry out combined measurement on the particles owned by the Alice and the Bob and publish the measurement results: in a quantum communication combined system, Alice and Bob form a particle pair by using two high-dimensional entangled-state particles shared by the Alice and the Bob and particles in an unknown particle state to be sent, generalized Bell measurement and generalized single particle measurement are carried out on the particles under a generalized Bell basis and a generalized single particle basis, and the Alice and the Bob publish respective measurement results through a classical channel. The measurement bases of the generalized Bell measurement and the generalized single particle measurement are respectively expressed as:
wherein n, m, j, l =0, 1, 2. The Bell measurement refers to that the internal product of particles is processed by using a Bell-based arbitrary vector and quantum communication combined system to obtain a measurement result.
After the Bell measurement is completed, the collapse state of the particle complex consisting of two high-dimensional entangled-state particles is determined.
And the measurement results of Alice and Bob are published by the classical channel, so that Alice obtains the measurement result of Bob, Bob obtains the measurement result of Alice, and the supervising party Charlie obtains the measurement results of both Alice and Bob.
In implementation, in the quantum communication joint system established in step 1, Alice and Bob combine the two high-dimensional particles shared by Alice and unknown high-dimensional quantum states to be transmitted into a particle pair, for example, in the quantum communication joint system in which the high-dimensional three-particle state and the high-dimensional four-particle state are used as quantum channels, Alice now performs generalized bayesian measurement on the particle pair (a, 1), and Bob performs generalized bayesian measurement on the particle pair (B, 4).
，
Particles 2, 3, B', 5, 6, 7 will collapse into
。
Step 3, the supervisor Charlie carries out single particle measurement on the particles owned by the supervisor Charlie and publishes the measurement result: according to the combined Bell measurement result of Alice under the Bell base and the combined Bell measurement result of Bob under the Bell base, the supervisor Charlie carries out single particle measurement on the owned particles respectively, and transmits the measurement result to Alice and Bob through a classical channel.
In implementation, the supervising party Charlie determines the measured corresponding collapse state through the obtained results of Alice and Bob measurement. And the supervising party Charlie carries out generalized single particle measurement on the owned particles on the basis of the collapse state, and transmits the measurement result to Alice and Bob through a classical channel.
Charlie performs generalized single particle measurement on the particle 2, and the measurement result is | Ψ（3）〉2Where l =0, 1, 2, k =0, 1, 2. After measurement the particles 3 will collapse into
. Bob respectively measures the particles B 'and Charlie on the particles 6 to obtain generalized single particle measurement results, wherein the measurement results of the particles B' are
， l1=0, 1, 2, particle 6 measurement result is
，l2=0, 1, 2 and delivers the measurement results to Alice and Bob via classical channels. Particles 5 and 7 will collapse to:
the method comprises the following steps of carrying out generalized single particle measurement on particles owned by a supervisor Charlie, and obtaining quantum information of the particles owned by the supervisor Charlie, so that the collapse state of a particle complex formed by two high-dimensional entangled-state particles is converted into the collapse state of the particle complex formed by the two high-dimensional entangled-state particles shared by Alice and Bob. Namely, with the help of Charlie of the Du side, Alice and Bob can recover the original quantum state of the received particles through the reconstruction of the particles owned by both sides.
And 4, constructing the full appearance of the original quantum state transmitted by the opposite party by using the measurement result by the Alice and the Bob: and the Alice and the Bob use the measurement results of the Alice and the other party and combine the monitoring party Charlie generalized single particle measurement result to separate the collapse state of the particle complex formed by the two high-dimensional entangled-state particles after measurement into a product state of the two high-dimensional entangled-state particle quantum information shared by the Alice and the Bob, and then reconstruct the original state of the other party through unitary transformation.
By calculation, it is possible to establish
And
the relation of the intermediate state, the unitary matrix used is:
the following can be obtained:
bob unitary operation U on particles 3 owned by the particlespqCan restore the standby state of Alice
Wherein p = n0 + l mod 3 ，q = 3 − m0 mod 3. Alice performs corresponding unitary operations (U) on the owned particles 5 and 70t）5 
（UST）7Thereby reducing the ready state of Bob
Where s = n1+ l1 + l2 mod 3，t = d − m1 mod d。
The implementation process of the method for the high-dimensional asymmetric bidirectional controlled quantum stealth state transfer is as follows. The implementation process can show that the bidirectional controlled invisible transmission method realizes the bidirectional transmission of quantum information in a high-dimensional space, increases the information quantity carried by unknown quantum states, only uses generalized Bell measurement and generalized single-particle measurement, realizes the reduction of the operation difficulty of quantum communication, and makes the bidirectional controlled invisible transmission state easier to physically realize.
It should be noted that, for simplicity of description, the above-mentioned embodiments of the method are described as a series of acts or combinations, but those skilled in the art should understand that the present application is not limited by the order of acts described, as some steps may be performed in other orders or simultaneously according to the present application. Further, those skilled in the art should also appreciate that the embodiments described in the specification are preferred embodiments and that the acts and elements referred to are not necessarily required in this application.
In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a ROM, a RAM, etc.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.
Claims (6)
1. A method for high-dimensional asymmetric bidirectional controlled quantum stealth state propagation is characterized by comprising the following steps:
step 1, establishing a quantum communication combination system based on Alice, Bob and Charlie: establishing a sender and a receiver of Alice and Bob in a high-dimensional single particle state and a high-dimensional two-particle state mutually, wherein Charlie is a monitor, two high-dimensional entangled states are used as quantum channels, and the Alice, the Bob and the Charlie share a quantum communication combined system of the two high-dimensional entangled states;
step 2, respectively carrying out generalized Bell measurement and generalized single particle measurement on the particles owned by Alice and Bob, and publishing the measurement results: in a quantum communication joint system, Alice and Bob form a particle pair by two shared high-dimensional entangled-state particles and a particle with an unknown particle state to be sent, correspondingly measure the particles, and publish the measurement results of Alice and Bob through a classical channel;
step 3, the supervisor Charlie carries out single particle measurement on the particles owned by the supervisor Charlie and publishes the measurement result: according to the measurement result of Alice and the measurement result of Bob, the supervisor Charlie respectively carries out single particle measurement on the owned particles and transmits the measurement result to Alice and Bob through a classical channel;
and 4, constructing the full appearance of the original quantum state transmitted by the opposite party by using the measurement result by the Alice and the Bob: and the Alice and the Bob use the measurement results of the Alice and the other party and combine the Charlie single-particle measurement result of the monitor to separate the collapse states of the particle complexes formed by the two high-dimensional particle states after measurement into the product states of the two high-dimensional entangled state quantum information shared by the Alice and the Bob, and then reconstruct the original states of the other party through unitary transformation.
2. The method according to claim 1, wherein the two high-dimensional entangled states in step 1 are quantum channels, and the two high-dimensional entangled states of quantum channels shared by Alice, Bob and Charlie adopt the maximum entangled state.
3. The method for the high-dimensional asymmetric bidirectional controlled quantum stealth transfer mode according to claim 1, wherein in step 1, Alice and Bob are both parties of quantum communication, and Alice and Bob are a sender and a receiver of unknown high-dimensional single-particle state and high-dimensional two-particle state, Alice serving as the sender sends the quantum state to Bob serving as the receiver, and Alice serving as the receiver receives the quantum state sent by Bob; charlie is a supervision party of quantum communication, under the control of Charlie, Alice reconstructs the quantum state transmitted by Bob, and Bob reconstructs the quantum state transmitted by Alice; particles in two high-dimensional entangled states as quantum channels are assigned to Alice, Bob, and Charlie.
4. The method according to claim 1, wherein Alice and Bob in step 4 construct an overall view of the original quantum state transmitted from the other party by using the measurement results, Alice and Bob construct a unitary transform by using their own and opposite measurement results and combining with a supervisory Charlie single-particle measurement result, perform single-particle measurement on the auxiliary particle, separate the collapse state of a particle complex consisting of two high-dimensional particle states after all measurements into a product state of two high-dimensional entangled-state quantum information shared by Alice and Bob, and reconstruct the original state of the other party by the unitary transform.
5. The method of claim 4, wherein the constructing of the unitary transform is specifically: alice performs a unitary transform on the measured collapsed state of the particle complexes with a high-dimensional unitary transform matrix with respect to Alice possessing high-dimensional entangled-state particles, and Bob performs a unitary transform on the measured collapsed state of the particle complexes with respect to Bob possessing high-dimensional entangled-state particles with a high-dimensional unitary transform matrix.
6. The method of claim 4, wherein reconstructing the original state of each other by unitary transformation comprises: and respectively applying unitary operation to the owned particles by Alice and Bob so as to realize the reconstruction of the original state of the particles.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115941058A (en) * | 2022-11-21 | 2023-04-07 | 成都理工大学 | Controlled bidirectional quantum invisible state transfer method |
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