CN104821875B - The high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding - Google Patents

The high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding Download PDF

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CN104821875B
CN104821875B CN201510250391.7A CN201510250391A CN104821875B CN 104821875 B CN104821875 B CN 104821875B CN 201510250391 A CN201510250391 A CN 201510250391A CN 104821875 B CN104821875 B CN 104821875B
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王川
王铁军
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Beijing University of Posts and Telecommunications
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Abstract

The present invention realizes a kind of high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding, constructs two unitary operators, provides two groups of complete intrinsic quantum states;Annular quantum secret sharing communication is carried out, based on intrinsic quantum state space, sender Alice prepares photon sequence and issues Bob at random;Bob randomly selects verification photon from photon sequence and carried outOrMeasurement, is encoded, photon issues Charlie after coding according to key word string to remaining photon;Charlie carries out verification photon survey to the photon sequence of reception, remaining photon is encoded according to key word string, photon issues Alice after coding;Alice judges whether communication channel is safe, reads Bob and Charlie and combines carried out encoding operation.The present invention increases the message capacity and spectrum efficiency of quantum secret sharing scheme using single photon orbital angular momentum, it is not necessary to multicomponent entangled photons state.

Description

High-capacity quantum secret sharing method based on photon orbital angular momentum coding
Technical Field
The invention belongs to the technical field of quantum communication, and particularly relates to a quantum secret sharing method based on photon orbital angular momentum high-dimensional coding.
Background
The classical secret sharing scheme is implemented in three parties, one of which is the master and needs to distribute the encryption key to both receivers, and since there may be an untrusted party, the receivers need to join together to read the encryption key. The existing quantum secret sharing scheme is implemented based on single photon polarization coding. In order to realize quantum secret information sharing, a sender of information uses two-component or three-component entangled photons as information bits, and then the entangled photons are transmitted through an optical fiber or free space and delivered to a receiver. The two parties are monitored safely and then a measuring base is selected randomly. Useful results can be obtained in case three parties select the same measurement reference at the same time. The receiving party jointly performs exclusive-or operation on the obtained secret information, and then the secret information sent by the leading party can be generated. In a traditional secret sharing scheme, the polarization degree of freedom of photons or the phase degree of freedom are utilized, and because the polarization degree of freedom and the phase degree of freedom of the photons are two-dimensional coding spaces, the coding capacity is limited, and the information transmission rate of quantum secret sharing is directly influenced.
Photon orbital angular momentum is proved by scientists in 1992 through experiments, and for electromagnetic waves with the same frequency, infinite values of different orbital angular momentums can be theoretically obtained. In 2010, Luhong, Coxizheng discloses research on quantum communication coding method of orbital angular momentum of light beams, and a quantum coding scheme is designed by utilizing orbital angular momentum of high-order Bessel diffraction-free light beams. 2012, guo jian army, guo bang hong, cheng guang and so on disclose "research progress of photon orbital angular momentum applied in quantum communication", introduced the quantum key distribution experimental scheme realized by utilizing photon orbital angular momentum, and provided an idea for the application of photon orbital angular momentum in quantum communication. At present, researchers have started to develop research by utilizing photon orbital angular momentum in a quantum key distribution scheme, and utilize photon orbital angular momentum to realize coding and complete secure transmission of a key, but at present, the problem of low channel transmission capacity in a secret sharing scheme of a storage quantum still exists, and orbital angular momentum is not applied to quantum secure direct communication at present to realize direct transmission of information.
Disclosure of Invention
The invention aims to overcome the defect of low channel transmission capacity in the existing quantum secret sharing scheme, and designs a high-capacity quantum secret sharing scheme for realizing information encoding and decoding by utilizing photon orbital angular momentum.
In order to achieve the above object, the present invention provides a high-capacity quantum secret sharing method based on photon orbital angular momentum coding, which is specifically realized by the following steps:
step 1: carrying out quantum state encoding;
setting the dimension of a high-dimensional measurement subspace as p, wherein a complete set of intrinsic quantum states are represented as { |0>, |1>, · and | p-1> }, and p is an integer greater than 2;
two unitary operators are constructed, respectively:
orbital angular momentum phase control operator in quantum spaceParameter ω ═ ei2π/p
Orbital angular momentum magnitude control operator in quantum space
The specific form of the quantum state code is constructed as two groups of complete intrinsic quantum states, and the form is expressed as follows:
{|t>t 0,1,2,.., p-1} and { | ψt>},
Wherein the parameter sjJ + (j +1) +. + (p-1), k represents any of 0,1, 2.
In the high-capacity quantum secret sharing method, quantum operation information is recorded by utilizing the orbital angular momentum quantum state of photons, and coding information is loaded as quantum operation through a unitary operator of a p-dimensional space.
Step 2: performing annular quantum secret sharing communication, and setting three communication parties as Alice, Bob and Charlie, wherein Alice sends the photon sequence to Bob, Bob sends the photon sequence to Charlie after the coding operation, and the Charlie sends the photon sequence to Alice after the coding operation; before communication starts, a dimension space p is selected in advance, and a specific communication process comprises a step 2.1 and a step 2.4.
Here Alice is the master (Boss) in the communication scheme, while Bob and Charlie are the receivers of both information.
Step 2.1: after communication begins, a sender Alice of information randomly prepares a group of photon sequences, wherein the orbital angular momentum state of each photon is randomly positioned in an intrinsic quantum state space { | t>T { | ψ, p-1}, or { | ψt>In (1) }; alice sends the prepared photon sequence to Bob.
Step 2.2: bob randomly selects a part of photons from the photon sequence as check photons after receiving a photon sequence, and the rest photons except the check photons in the photon sequence are the photons to be coded; bob randomly checks the photons atOr/andmeasuring the space; then Bob randomly encodes the photons to be encoded, and sends the encoded photons to Charlie.
Bob carries out encoding operation on the photons to be encoded according to the own secret key string, specifically: randomly selecting the orbital angular momentum of the photon to be coded according to an h-system information sequence needing to be transmittedOrIs operated byOperating to encode logical bit 0, usingThe operation encodes a logical bit h, whereIs an identity matrix, and the value range of h is (1, 2.., p-1).
Step 2.3: after receiving the photon sequence coded by Bob, Charlie randomly selects a part of the photon sequence as a check photon, and the rest photons except the check photon in the photon sequence are the photons to be coded; charlie checks photon at randomOr/andmeasuring the space; and then, Charlie randomly encodes the photons to be encoded and sends the encoded photons to Alice.
Charlie carries out coding operation on the photon to be coded according to the key string of the Charlie, and the orbital angular momentum of the photon to be coded is randomly selected according to the h-system information sequence needing to be transmittedOrIs operated byOperating to encode logical bit 0, usingThe operation encodes a logical bit h.
Step 2.4: and after receiving the photon sequence, Alice compares the position of the verified photon, the measurement base and the measurement result with Bob and Charlie through a public channel respectively, and judges whether the bit error rate is lower than the safety threshold of the communication channel, if so, the communication channel is safe, otherwise, the communication channel is unsafe.
When the communication channel is safe, Alice compares the initial state and the final state of the photon orbital angular momentum, reads the coding operation carried out by the combination of Bob and Charlie, and the secret key of Alice is the product of the coding secret keys of Bob and Charlie; when the communication channel is not secure, the communication is stopped.
Compared with the prior art, the invention has the advantages and positive effects that:
(1) quantum information encoding and decoding of photon orbital angular momentum are realized by utilizing the holographic plate and the linear optical element;
(2) high-dimensional quantum secret sharing of an annular distribution mode based on photon orbital angular momentum is realized, and communication capacity and spectral efficiency of a quantum secret sharing scheme are improved by utilizing single photon orbital angular momentum coding;
(3) the invention expands the encoding space of secret information to an N-dimensional system, realizes the quantum secret sharing scheme of the annular distribution mode in the orbital angular momentum space of single photons, has higher efficiency, does not need multi-component entangled photon state, and has stronger realizability.
Drawings
FIG. 1 is a schematic diagram of an orbital angular momentum separator;
FIG. 2 is a schematic diagram of an encoding device in a five-dimensional space based on the quantum secret sharing method of orbital angular momentum;
FIG. 3 is a schematic diagram of three communication parties of the quantum secret sharing method based on orbital angular momentum of the invention;
fig. 4 is a flow chart of the quantum secret sharing method based on orbital angular momentum.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The core of the invention is that the photon orbital angular momentum, which is the electromagnetic wave parameter dimension, is used in the quantum secret sharing scheme, and the photon orbital angular momentum is utilized to improve the spectrum communication efficiency and capacity of the quantum secret sharing system.
Fig. 1 is an orbital angular momentum separator, which can realize the control of orbital angular momentum in two-dimensional space. In fig. 1: CPBS denotes a circularly polarized light polarizing beam splitter, PBS denotes a polarized light polarizing beam splitter, R denotes a mirror, and DP denotes a Dove prism. Photon quantum state of incident port of orbital angular momentum separator can be markedWherein | H>Indicating that the polarization of the photon is in a horizontally polarized state, |>The value representing the orbital angular momentum of this photon is l. When a photon passes through the CPBS device, its left-hand and right-hand circularly polarized components will be separated, its left-hand photon state will pass through path 1, and its right-hand photon state will pass through path 2. Path 1 refers to the path connected to the right side of the CPBS apparatus in fig. 1, and path 1 sequentially passes through one DP and one R and reaches the PBS. Path 2 refers to the path connecting the bottom of the CPBS device in fig. 1, and path 2 sequentially passes through an R and a DP to reach the PBS.
In the device, the optical axes of the Dove prisms on the path 1 and the path 2 have a relative α angle difference, two paths of circularly polarized light respectively pass through the Dove prisms and are combined into one path of output through the PBS, and the final state is changed into that:a suitable value of α can be adjusted to α ═ pi/2)/(l1-l2) Finally, two state components of the photon can be obtained through two ports of the PBS, which are:andwherein l ═ l1+l2)。l1And l2The orbital angular momentum values of the two photons are positive integers less than l.
The device on which the method of the invention is based comprises an encoding module, as shown in figure 2, and a decoding module, which is the inverse of the encoding module. In the embodiment shown in fig. 2, communication is performed in a quantum space with a dimension p of 5, a sender cascades 5 devices shown in fig. 1, and photon components with different orbital angular momentums l are output along different paths through the cascaded orbital angular momentum separator devices, wherein the paths are marked with different orbital angular momentum values from top to bottom in sequence. In the embodiment shown in fig. 2: omega0~ω4Sequentially representing different path degrees of freedom, wherein a Cascaded OAM sorter represents a Cascaded orbital angular momentum separator, and a Reversed configuration represents the reverse process of an OAM sorter cascade device. On each way, can proceedOr/andin whichIs a phase shift operation, which can be done by a phase shift plate;the conversion between quantum states with different orbital angular momentum can be realized by the combined action of the quarter-wave plate and the holographic plate.
The invention relates to a ring quantum secret sharing method based on photon orbital angular momentum coding, which is based on a device comprising an encoding module and a decoding module, wherein the encoding module is implemented as shown in figure 2, and the decoding module is the inverse process of the encoding module.
The high-capacity quantum secret sharing method based on photon orbital angular momentum coding of the invention is specifically explained as follows by combining fig. 3 and fig. 4.
Step 1: and carrying out quantum state coding.
Let the dimension of the high-dimensional metric subspace be p, where a complete set of intrinsic quantum states can be represented as { |0>, |1>, · |, | p-1> }, p is a natural number greater than 2.
In this quantum space, two unitary operators can be constructed, in particular:
and
wherein, j is a natural number smaller than p and is used for representing the state of photon orbital angular momentum.
Representing the angular momentum phase control operator in quantum space,representing an angular momentum magnitude control operator in quantum space. WhereinThe phase of the orbital angular momentum of a particular photon can be changed,the size of the orbital angular momentum of the photon can be changed; parameter ω ═ ei2π/p
Further, a specific form of a coding state is constructed, the coding space is p-dimensional, the coding states are two complete sets of intrinsic quantum states, and the form can be expressed as { | t>T 0,1,2,.., p-1} and { | ψt>ThereinWherein the parameter sjJ + (j +1) +. + - (p-1), t ═ 0,1, 2.., p-1, where superscript k denotes any of 0,1, 2.., p-1.
In the method, information to be transmitted is encoded on quantum states, and the encoding operation is completed through a unitary operator of a p-dimensional space.
Step 2: and carrying out annular quantum secret sharing.
The three communication parties are Alice, Bob and Charlie, and FIG. 3 shows a schematic diagram of ring quantum secret sharing of the invention, wherein an information source Alice sends a photon sequence to Bob, Bob sends to Charlie after encoding operation, and sends to Alice after Charlie encoding operation, thereby forming a ring communication mode.
Step 2.1: a dimension space p is selected in advance by the three communication parties Alice, Bob and Charlie; p is an integer greater than 2. After communication begins, Alice randomly prepares a set of photon sequences comprising n photons, each photon having a quantum state ofAnd the prepared photon sequence is sent to Bob by Alice through the quantum channel.
The orbital angular momentum state of each photon in the photon sequence prepared by Alice is randomly inOrIs the eigen quantum state space { | t>T { | ψ, p-1}, or { | ψt>In (c) }.
Step 2.2: after receiving the photon sequence sent by Alice, Bob randomly selects a part of the photon sequence as a check photon, and the rest photons except the check photon in the photon sequence are the photons to be coded by Bob. Checking lightThe security check is performed. Bob takes the path of the check photons using the apparatus shown in FIG. 2Or/andobtaining a measurement result of the check photons; after the measurement is finished, Bob encodes photons according to the key string k of BobBAnd carrying out an encoding operation, and sending the photons which complete the encoding operation to Charlie by Bob.
The specific encoding operation is: randomly selecting the orbital angular momentum of the photon to be coded according to an h-system information sequence needing to be transmittedOrIs operated byThe operation encodes a logical bit of 0 and,is an identity matrix, which means that no operation is performed; by usingThe operation encodes a logical bit h, where h has a value range of (1, 2.., p-1). For example, the orbital angular momentum of the photon is | ψt>The operation encodes a logical bit h, which can be expressed mathematically asDirectly multiplying by | ψt>。
In the embodiment of the present invention, p is 5, as shown in fig. 2, Bob cascades p orbital angular momentum separators shown in fig. 1, and the check photons pass through p cascaded tracksThe photon components of different orbital angular momentum values output by the orbital angular momentum separator are output along different paths, and the paths are marked with orbital angular momentum values omega corresponding to the output after the operation in the orbital angular momentum separatorj. In the orbital angular momentum separator corresponding to each path, corresponding operation is carried outOr/andin whichThe operation is performed by means of a phase-shift plate,the operation is realized by the combined action of the quarter-wave plate and the holographic plate.
The check photon does not need encoding operation, and the check photon is measured to obtain the orbital angular momentum of the photon for safety detection.
Step 2.3: and after receiving the photon sequence sent by Bob, Charlie repeats the operation process of Bob, codes the received photon sequence and sends the coded photon sequence to Alice.
After receiving the photon sequence sent by Bob, Charlie is similar to Bob, and a part of photons are randomly selected from the photon sequence to be used as check photons, so that the rest photons except the check photons in the photon sequence are the photons to be coded of Charlie. Charlie pairs of check photons were performed randomly using an orbital angular momentum separator on each path using the apparatus shown in FIG. 2Or/andand (4) obtaining the orbital angular momentum state of the check photon.
After the measurement is finished, Charlie is used for coding photons according to the key string k of the CharlieCAn encoding operation is performed.
The encoding process is the same as the operation of Bob, and the orbital angular momentum of photons is randomly selected according to an h-system information sequence needing to be transmittedOrIs operated byOperating to encode logical bit 0, usingThe operation encodes a logical bit h.
Charlie sends the encoded photons back to Alice after the encoding operation is completed.
Step 2.4: and after receiving the photons, Alice compares the positions of the verified photons, the measurement bases and the measurement results with Bob and Charlie through the public channel respectively to carry out communication channel safety verification. When the communication channel is secure, Alice compares the initial state and the final state of the photon orbital angular momentum, and reads the encoding operation performed by Bob and Charlie jointly. When the communication channel is not secure, the communication is stopped.
And after receiving the photons, Alice compares the positions of the photons with Bob and Charlie respectively through the public channel to check the positions of the photons, measure the base and measure the result. And judging whether the bit error rate is lower than a safety threshold value of the channel or not according to the measurement result, if so, determining that the communication channel is safe, otherwise, determining that the communication channel is unsafe.
Since Alice is the producer of the bits, Alice knows the initial orbital angular momentum state of each photon as determined. Alice selects an intrinsic quantum state space { | t according to photon preparation>T is 0,1,2,.., p-1} or { | ψt>And measuring the orbital angular momentum of the received photons in the intrinsic quantum state space, thereby reading out the final orbital angular momentum state of the photons. Comparing the initial orbital angular momentum state and the final orbital angular momentum state of the photon, Alice can read the coding operation performed by the combination of Bob and Charlie, namely reading out the coding key of Bob and CharlieThereby constructing key bit information. To this end, the secret sharing scheme is complete, with Alice's key being the product of Bob's and Charlie's encoding keys.

Claims (2)

1. A high-capacity quantum secret sharing method based on photon orbital angular momentum coding is characterized in that the sharing of high-capacity quantum secret information is realized by utilizing orbital angular momentum quantum state coding, and the method comprises the following steps:
step 1: carrying out quantum state encoding;
setting the dimension of the high-dimensional measurement subspace as p, wherein p is an integer greater than 2;
constructing orbital angular momentum phase control operators in quantum spaceParameter ω ═ ei2π/pω represents a path degree of freedom;
orbital angular momentum magnitude control operator in construction quantum space
The specific form of the quantum state code is constructed as two groups of complete intrinsic quantum states, and the form is expressed as follows:
{|t>t 0,1,2,.., p-1} and { | ψt>};
Wherein,parameter sjJ + (j +1) +. + (p-1), k represents any of 0,1, 2., p-1;
step 2: performing annular quantum secret sharing communication, and setting three communication parties as Alice, Bob and Charlie, wherein Alice sends the photon sequence to Bob, Bob sends the photon sequence to Charlie after encoding operation, and the Charlie sends the photon sequence to Alice after encoding operation; before communication begins, a dimension space p is selected in advance, and the specific communication process comprises steps 2.1-2.4;
step 2.1: alice randomly prepares a set of photon sequences in which the orbital angular momentum state of each photon randomly lies in the space of intrinsic quantum statesOrPerforming the following steps; the Alice sends the prepared photon sequence to Bob;
step 2.2: after Bob receives the photon sequence, randomly selecting a part of photons from the photon sequence as check photons, and taking the rest photons except the check photons in the photon sequence as photons to be coded; bob randomly checks the photons atOr/andmeasuring the space to obtain the orbital angular momentum state of the check photon; then Bob randomly encodes the photons to be encoded, and sends the encoded photons to Charlie;
bob carries out encoding operation on the photons to be encoded according to the own secret key string, specifically: randomly selecting the orbital angular momentum of the photon to be coded according to an h-system information sequence needing to be transmittedOrIs operated byOperating to encode logical bit 0, usingThe operation encodes a logical bit h, whereIs an identity matrix, and the value range of h is (1, 2.., p-1);
step 2.3: after receiving the photon sequence coded by Bob, Charlie randomly selects a part of the photon sequence as a check photon, and the rest photons except the check photon in the photon sequence are the photons to be coded;
charlie checks photon at randomOr/andmeasuring the space; then, Charlie randomly encodes the photons to be encoded and sends the encoded photons to Alice;
charlie carries out coding operation on the photon to be coded according to the key string of the Charlie, and the orbital angular momentum of the photon to be coded is randomly selected according to the h-system information sequence needing to be transmittedOrIs operated byOperating to encode logical bit 0, usingOperating the encoded logic bit h;
step 2.4: after receiving the photon sequence, Alice compares the position of the verified photon, the measurement basis and the measurement result with Bob and Charlie through a public channel respectively, and judges whether the bit error rate is lower than the safety threshold of the communication channel, if so, the communication channel is safe, otherwise, the communication channel is unsafe;
when the communication channel is safe, Alice compares the initial state and the final state of the photon orbital angular momentum, reads the coding operation carried out by the combination of Bob and Charlie, and the secret key of Alice is the product of the coding secret keys of Bob and Charlie; when the communication channel is not secure, the communication is stopped.
2. The method for realizing high-capacity quantum secret sharing based on photon orbital angular momentum coding according to claim 1, wherein the sender Alice concatenates p orbital angular momentum separators, and the check photons pass through the p cascaded orbital angular momentum separators to be randomly performedOr/andoperation in whichThe operation is performed by means of a phase-shift plate,the operation is realized by the combined action of the quarter-wave plate and the holographic plate; outputting photon components of different orbital angular momentum values along different paths, wherein the paths are marked with corresponding orbital angular momentum values omegaj
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