CN109617620B - Multi-hop quantum invisible state transfer method based on channel error correction - Google Patents

Multi-hop quantum invisible state transfer method based on channel error correction Download PDF

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CN109617620B
CN109617620B CN201910137579.9A CN201910137579A CN109617620B CN 109617620 B CN109617620 B CN 109617620B CN 201910137579 A CN201910137579 A CN 201910137579A CN 109617620 B CN109617620 B CN 109617620B
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付粉香
姜敏
夏志新
孙兵
黄旭
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Abstract

The invention discloses a method based onThe multi-hop quantum invisible state transfer method for channel error correction is characterized by comprising the following steps: the two communication parties are an information sender Alice and an information receiver Bob, and the particle src carries unknown quantum state information | χ>src＝a|0>+b|1>The information sender Alice holds the unknown single-particle quantum state and wants to send the unknown single-particle quantum state to the receiver Bob; the sender Alice holds a particle src and a particle 1, the 1 st intermediate node holds a particle 2 and a particle 3, the 2 nd intermediate node holds a particle 4 and a particle 5, …, and the i (i ═ 1,2,3, …, N) th intermediate node holds a particle 2i and a particle 2i +1, where N is a positive integer. The invention has the following beneficial effects: firstly, the error correction operation and the original unknown quantum state recovery operation are uniformly executed by the information receiver Bob, the error correction operation is not required to be performed by an intermediate party, the intermediate party only needs Bell measurement, the operation requirement of the intermediate party is simplified, and the complexity of constructing a quantum communication network is reduced.

Description

Multi-hop quantum invisible state transfer method based on channel error correction
Technical Field
The invention relates to a communication network and an information transmission method, in particular to a multi-hop quantum invisible state transmission method based on channel error correction.
Background
Quantum communication is a novel communication mode for information transmission by using a quantum entanglement effect, the main body of transmitted information is quantum information or classical information, and a channel is a quantum channel or a quantum channel assisted with the classical channel. The research directions of Quantum communication mainly include Quantum invisible state (Quantum cryptography) 1, Quantum cryptography 2, Quantum Dense Coding 3-6, and the like.
The concept of quantum invisible state was proposed by several scientists of Bennett, Brassard, etc. in 1993, and quantum entanglement property was utilized to realize quantum invisible state, thereby opening the way to research quantum invisible state. The quantum invisible transport theory indicates that: by utilizing quantum entanglement phenomenon, the information of unknown quantum state can be sent out without transmitting any physical quantum bit, and the information transmission of the hyperspace is realized. In an initial quantum invisible state communication system, a sender Alice exists, which holds an unknown quantum state to be transmitted, a receiver Bob exists, two communication parties are in spatially separated states, but share an EPR quantum pair, and joint Bell-based measurement is carried out on one particle of the transmitted unknown quantum state and the EPR entangled pair.
In recent years, with the increasingly deep research of point-to-point quantum communication, quantum communication is also gradually going to the development direction of networking. According to the definition of SECoQC [7] (Development of a Global Network for Secure communication on Quantum Cryptography), a Quantum Network is based on point-to-point Quantum key distribution, so that two communication parties in the Network can exchange theoretically Secure keys instead of an infrastructure for Secure communication. The quantum communication network comprises a plurality of quantum relay nodes, every two adjacent relay nodes are connected by a section of entangled channel to form a chain channel, all the relay nodes on the source node and the quantum path carry out Bell measurement on the own particles, and finally the transmitted unknown quantum state is restored on the particles held by the destination node, so that the communication between the two nodes can be finally realized based on an EPR protocol. Quantum communication networks have several significant advantages over classical communication networks: (1) the security and confidentiality of communication are higher; (2) the communication efficiency is higher due to stronger information transmission and processing capacity; (3) the communication complexity is low. Currently, many groups of research have proposed their own ideas for constructing quantum networks. Cheng et al [8] propose a routing mechanism for hierarchical network structures to deliver a quantum state information at two nodes that do not directly share entanglement pairs; wang et al [9] propose a quantum wireless multi-hop invisible state transfer system based on any Bell pairs, which is used for constructing a quantum communication network; the Guo brilliant [10-13] research group of the Chinese science and technology university and the PanJianwei [14-17] team of the Chinese science and technology university are dedicated to research on the physical implementation of quantum communication networks.
In an actual quantum communication network, due to the interaction between particles and the environment, the quantum state of the particles can be changed under the influence of quantum noise in the process of channel transmission, and the quantum dislocation which can be generated by the action of a qubit and the environment can be as follows [18 ]:
i-no error; the X-bit is anti-error;
a Z-phase fault; XZ-bit anti-faulting + bit faulting
Based on this, quantum communication network needs to adopt quantum error correction technology to ensure the reliable transmission of the original unknown quantum state information, and it realizes the protection to the quantum channel based on the quantum mechanics principle, and can ensure the absolute reliability of the communication between two places. The invention provides a multi-hop quantum invisible state transfer method based on channel error correction, wherein each communication node on a communication path directly sends errors generated by quantum bits to an information receiver, and the information receiver executes appropriate matrix transformation to correct quantum errors and correctly recover transmitted unknown quantum state information.
The present invention is described in the following references
[1]Bennett C H，Bmssard G，Crepeau C，et a1.Teleporting an unknownquantum state via dual classical and Einstein-Podolsky-Rosen channels[J].Physical Review Letters，1993,70(13):1895-1899.
[2]A.K.Ekert,Quantum Cryptography Based on Bell’s Theorem.PhysicalReview Letters,1991,67(6):661-663.
[3]C.H.Bennett,Communication via one and two-particle operators onEPR states.Phys.Rev.Lett.69(1992)2881-2884.
[4]Moore C,Nilsson M.Parallel Quantum Computation and QuantumCodes.SIAM Journal on Computing,2001,31(3):799–815.
[5]Yeo Y,Chua W K.Teleportation and Dense Coding with GenuineMultipartite Entanglement.Physical Review Letters,2006,96(6):060502.
[6]Rigolin G.Superdense coding using multipartite states,2004.http://www.citebase.org/abstract？id＝oai:arXiv.org:quant-ph/0407193.
[7]M Peev,C Pacher,R Alléaume,et al.The SECOQC quantum keydistribution
network in Vienna.New.J.Phys.11,(2009)075001.
[8]Sheng-Tzong Cheng,Chun-Yen Wang,Ming-Hon Tao.Quantum communicationfor wireless wide-area networks[J],IEEE.Journal on Selected Areas inCommunications,2005,23(7):1424-1432.
[9]Kan Wang，Xu-Tao Yu,Sheng-Li Lu,Yan-Xiao Gong.Quantum wirelessmultihop communication based on arbitrary Bell pairs and teleportation.[J].Physical Review A，2014,89(2A):1-10.
[10]LU H,GUO G C.Teleportation of two-particle entangled state viaentanglement swapping[J].PhysLett A,2000,276:209.
[11]YANG C P,GUO G C.Multi-particle generalization of teleportation[J].Chin PhysLett,2000,17:162.
[12]ShengLi Zhang；XuBo Zou；JianHong Shi；JianSheng Guo；GuangCanGuo.Quantum illumination in the presence of photon loss.Physical Review A:Atomic,Molecular&Optical Physics,2014,Vol.90,No.5A:1-5.
[13]Meng Li,Yunfeng Huang,Guangcan Guo.Quantum Correlations EvolutionAsymmetry in Quantum Channels[J].Communications in Theoretical Physics,2017(3).
[14]PAN J W,BOUWMEESTER D,WEINFURTER Heta1.Experimental entanglementswapping：Entangling photons that never interacted[J].Physical Review Letters，1998，80(18)：3891-3894.
[15]Chao-Yang Lu and Jian-Wei Pan.Quantum optics:Push-button photonentanglement.Nature Photonics,2014,Vol.8,No.3:174-176.
[16]Xiu-Xiu Xia；Qi-Chao Sun；Qiang Zhang and Jian-Wei Pan.Longdistance quantum teleportation.Quantum Science and Technology,2017,Vol.3,No.1:014012.
[17]Qi-Chao Sun,Ya-Li Mao,Jian-Wei Pan et.al.Quantum teleportationwith independent sources and prior entanglement distribution over anetwork.Nature Photonics,Vol.10,No.10:671-675.
[18] Analysis and research of quantum error correction technology of Lujing, Zhao Yuan east, Yang Xiong, stabilizer, Microcomputer journal of information, Vol.26,2005.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a multi-hop quantum invisible state transfer method based on channel error correction, which realizes the channel error correction of a quantum communication network, so as to ensure the reliable transmission of the original unknown quantum state information and ensure the absolute reliability of the communication between two places.
In order to solve the technical problem, the invention provides a multi-hop quantum invisible state transfer method based on channel error correction, which comprises the following steps:
(1) communication channel construction: the two communication parties are an information sender Alice and an information receiver Bob, and the particle src carries an unknown quantum state | χ>src＝a|0>+b|1>The information sender Alice holds the unknown single-particle quantum state and wants to send the unknown single-particle quantum state to the receiver Bob; the sender Alice holds a particle src and a particle 1, the 1 st intermediate node holds a particle 2 and a particle 3, the 2 nd intermediate node holds a particle 4 and a particle 5, …, and the i (i ═ 1,2,3, …, N) th intermediate node holds a particle 2i and a particle 2i +1, where N is a positive integer; a receiver Bob at the target node holds particles 2N + 2; every two adjacent nodes share the same two-bit Bell state quantum channel to form a chain communication channel; the channel form is:
Figure BDA0001977431310000051
due to the interaction between the particles and the surrounding environment, the quantum state may be changed by the influence of quantum noise during the channel transmission process, so as to generate quantum dislocation, and the dislocation information may be one of four types, I, X, Z and XZ.
(2) Bell measurement: the source node Alice and the N intermediate nodes simultaneously execute combined Bell measurement on two particles owned by the source node Alice and the N intermediate nodes, and four measurement results can be respectively obtained;
(3) information transmission: the source node Alice and the N intermediate nodes simultaneously send dislocation information (one of four types including I, X, Z and XZ) generated by the particles held by the source node Alice and the N intermediate nodes and the Bell measurement result of the source node Alice and the N intermediate nodes to the receiver Bob;
(4) dislocation correction, information recovery: bob determines an error correction matrix according to the received error information of all the qubits, and combines the Bell measurement result information of each node to obtain the quantum system with the state:
Figure BDA0001977431310000052
wherein the content of the first and second substances,
Figure BDA0001977431310000053
represents the Bell measurement result of the i (i-1, 2, …, N +1) th node.
In one embodiment, "bit error correction, information recovery: "in, suppose quantum channel
Figure BDA0001977431310000061
The qubit errors generated by the entangled particles 2i-1 and 2i of (1) are: u shapei0,Ui1(i ═ 1,2, …, N +1), and is present
Ui0Ui1＝Ui(i＝1,2,…,N+1)
Wherein, Ui0,Ui1All belong to one of four kinds of quantum bit errors of I, X, Z and XZ;
then Bob obtains an error correction matrix according to the received error information of all qubits as follows:
Ucor＝UN+1UN…U1。
in one embodiment, "bit error correction, information recovery: "wherein, when i is 1,
Figure BDA0001977431310000062
indicating the sender of information AliceAnd particle 0 is the original carrier particle of unknown quantum state to be transmitted
Figure BDA0001977431310000063
Indicates that when the ith (i-1, 2, …, N +1) node measures the own particles 2i-2 and 2i-1
Figure BDA0001977431310000064
Then, Bob needs to perform on the particle 2N +2 held by Bob
Figure BDA0001977431310000065
A matrix transformation operation;
Figure BDA0001977431310000066
is of the matrix form:
Figure BDA0001977431310000067
regardless of the global phase of the quantum state, the information receiver Bob performs a matrix operation on the particle 2N +2 it holds
Figure BDA0001977431310000068
I.e. the transmitted unknown quantum state information can be recovered.
The invention has the beneficial effects that:
1. according to the multi-hop quantum invisible state transfer method based on channel error correction, all nodes on a communication path can simultaneously carry out Bell measurement, and simultaneously, dislocation information and Bell measurement results are sent to a target node, so that the efficiency of information transmission is improved.
2. According to the multi-hop quantum invisible state transfer method based on channel error correction, error correction operation and original unknown quantum state recovery operation are uniformly executed by the information receiver Bob, error correction operation is not required by an intermediate party, the intermediate party only needs Bell measurement, operation requirements of the intermediate party are simplified, complexity of quantum communication network construction is reduced, and requirements of complex quantum communication network construction can be met.
Drawings
Fig. 1 is a flowchart of a multi-hop quantum invisible state transfer method based on channel error correction according to the present invention.
Fig. 2 is a particle distribution diagram of the multi-hop quantum invisible state transfer method based on channel error correction according to the present invention.
Fig. 3 is a schematic diagram of a multi-hop quantum invisible transport protocol based on channel error correction according to the present invention.
Fig. 4 is a schematic diagram of particle distribution of a two-hop stealth transmission system based on channel error correction according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of particle distribution of a three-hop stealth dynamic system based on channel error correction according to a second embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The technical terms of the invention explain:
1. bell state
The Bell state is the maximum entangled state formed by two energy-level two particles, and forms a set of complete orthogonal bases of a two-dimensional Hilbert space, and four types of Bell measurement bases used in quantum communication are represented as follows:
Figure BDA0001977431310000081
Figure BDA0001977431310000082
Figure BDA0001977431310000083
Figure BDA0001977431310000084
2. controlled NOT gate
A quantum controlled not gate (CNOT gate) is a typical multi-qubit quantum logic gate that has two input qubits, a control qubit and a target qubit. The function is as follows: the control qubit remains unchanged and the target qubit is the result of modulo-2 addition of the control qubit with the target qubit. The matrix form corresponding to the two-level controlled NOT gate is as follows:
Figure BDA0001977431310000085
3. h-shaped door
The invention uses two-level H-gate operation, which is embodied as follows:
Figure BDA0001977431310000086
the effect of the two-level H gate is to gate |0>Change to |0>To |1>Intermediate state of (2)
Figure BDA0001977431310000087
And handle |1>Change to be also |0>To |1>Intermediate state of (2)
Figure BDA0001977431310000088
4. Quantum bit error
A qubit and environmental interaction may produce the following dislocations:
i: no error X: bit anti-error
Z: bit error XZ: bit inverse error + bit error
The matrix forms of several kinds of quantum bit errors are respectively:
Figure BDA0001977431310000091
a multi-hop quantum invisible state transfer method based on channel error correction comprises the following steps:
1. a multi-hop quantum invisible state transfer method based on channel error correction is characterized in that: it comprises the following steps:
step 1, communication channel construction. The two communication parties are an information sender Alice and an information receiver Bob, and the particle src carries an unknown quantum state | χ>src＝a|0>+b|1>The information sender Alice holds the unknown single-particle quantum state and wants to send the unknown single-particle quantum state to the receiver Bob. The sender Alice holds a particle src and a particle 1, the 1 st intermediate node holds a particle 2 and a particle 3, the 2 nd intermediate node holds a particle 4 and a particle 5, …, and the i (i ═ 1,2,3, …, N) th intermediate node holds a particle 2i and a particle 2i +1, where N is a positive integer; receiver Bob at the destination node holds particle 2N + 2. Every two adjacent nodes share the same two-bit Bell state quantum channel, and a chain communication channel is formed. The channel form is:
Figure BDA0001977431310000092
during channel allocation or formation, quantum dislocations may be generated, and the dislocation form is one of four types I, X, Z, XZ.
Step 2.Bell measurement: the source node Alice and the N intermediate nodes simultaneously execute combined Bell measurement on two particles owned by the source node Alice and the N intermediate nodes, and four measurement results can be respectively obtained;
and step 3, information transmission: the source node Alice and the N intermediate nodes simultaneously send dislocation information (one of four types including I, X, Z and XZ) generated by the particles held by the source node Alice and the N intermediate nodes and the Bell measurement result of the source node Alice and the N intermediate nodes to the receiver Bob;
step 4, dislocation correction and information recovery: first, Bob determines the error correction matrix from the error information of all the received qubits, without loss of generality, assuming a quantum channel
Figure BDA0001977431310000093
The qubit errors generated by the entangled particles 2i-1 and 2i of (1) are: u shapei0,Ui1(i ═ 1,2, …, N +1), and is present
Ui0Ui1＝Ui(i＝1,2,…,N+1)
Wherein, Ui0,Ui1All belong to one of four kinds of quantum bit errors of I, X, Z and XZ.
The error correction matrix obtained by Bob according to the received error information of all the qubits is:
Ucor＝UN+1UN…U1
secondly, by combining the Bell measurement result information of all the nodes, the quantum system state can be obtained as follows:
Figure BDA0001977431310000101
wherein the content of the first and second substances,
Figure BDA0001977431310000102
represents the Bell measurement result of the i (i-1, 2, …, N +1) th node. In particular, when i is 1,
Figure BDA0001977431310000103
the Bell measurement result of the information sender Alice is represented, and the particle 0 is the carrier particle src of the original unknown quantum state to be transmitted.
Figure BDA0001977431310000104
Indicates that when the ith (i-1, 2, …, N +1) node measures the own particles 2i-2 and 2i-1
Figure BDA0001977431310000105
Then, Bob needs to perform on the particle 2N +2 held by Bob
Figure BDA0001977431310000106
A matrix transformation operation.
Figure BDA0001977431310000107
Is of the matrix form:
Figure BDA0001977431310000108
regardless of the global phase of the quantum state, the information receiver Bob performs on the particle 2N +2 it holdsMatrix operations
Figure BDA0001977431310000109
I.e. the transmitted unknown quantum state information can be recovered.
The multi-hop quantum invisible state transfer method based on channel error correction is suitable for the technical field of quantum communication networks and information transmission.
The first embodiment is as follows: a multi-hop quantum invisible state transmission method based on channel error correction takes a two-hop invisible state as an example to realize that an information sender Alice transmits an unknown single-particle state | χ to an information receiver Bob>srcThe method comprises the following specific steps:
step 1: and constructing a two-hop quantum invisible state channel. The two communication parties are an information sender Alice and an information receiver Bob, and the particle src carries an unknown quantum state | χ>src＝a|0>+b|1>The information sender Alice holds the information. Alice wants to directly send the unknown single-particle quantum state to an information receiver Bob, and the entanglement channel of Alice and Bob is as follows:
Figure BDA0001977431310000111
it is assumed that qubit errors generated by the quantum entanglement channels of the information sender Alice and the information receiver Bob are X, Z, respectively.
Step 2: bell measurement: and the information sender Alice performs combined Bell-based measurement on the own particle src and particle 1, so that the transmitted original unknown quantum state is restored on the particle 2 held by the receiver Bob. Transferred unknown quantum state | ×>srcChannel entangled with quantum
Figure BDA0001977431310000114
And performing tensor product operation, wherein the states of the three particles after the operation are represented as:
Figure BDA0001977431310000112
the information sender Alice performs a joint Bell-based measurement on the own particle src and particle 1, possibly obtaining four measurement results, and correspondingly, particle 2 collapses to four quantum states:
Figure BDA0001977431310000113
and step 3: and (5) information transmission. And the Alice sends the self quantum bit error information and the Bell measurement result information to Bob.
And 4, step 4: and (4) dislocation correction and information recovery. Based on the qubit error information sent by Alice, Bob may determine the error correction matrix as Ucor＝U1XZ. So that the whole quantum invisible state transfer system has the following form:
Figure BDA0001977431310000121
wherein, by
Figure BDA0001977431310000122
The following results were obtained:
U00＝|0><0|+|1><1
U10＝|0><0|-|1><1
U01＝|0><1|+|1><0
U11＝|0><1|-|1><0
regardless of the global phase of the quantum state, the information receiver Bob performs a matrix operation on the particles 2 it holds
Figure BDA0001977431310000123
I.e. the transmitted unknown quantum state information can be recovered.
Example two: a multi-hop quantum invisible state transmission method based on channel error correction takes a three-hop invisible state as an example to realize that an information sender Alice transmits an unknown single-particle state | χ to an information receiver Bob>srcThe method comprises the following specific steps:
step 1: and constructing a three-hop quantum invisible transmission channel. The communication path is provided with an information sender Alice, an intermediate node and an information receiver Bob, and the particle src carries an unknown quantum state | χ>src＝a|0>+b|1>From informationThe sender Alice holds. Alice wants to send the unknown single-particle quantum state to an information receiver Bob through an intermediate node. The entanglement channel between Alice and the intermediate node is as follows:
Figure BDA0001977431310000124
the entanglement channels of the intermediate node and Bob are:
Figure BDA0001977431310000125
suppose particles 1,2,3,4 produce qubit errors XZ, X, Z, respectively.
Step 2: bell measurement: the information sender Alice and the intermediate node respectively execute combined Bell-based measurement on the two particles owned by the information sender Alice and the intermediate node, so that the transmitted original unknown quantum state is restored on the particles 4 held by the receiver Bob. Transferred unknown quantum state | ×>srcChannel entangled with quantum
Figure BDA0001977431310000131
For the tensor product operation, the states of the five particles after the operation are represented as:
Figure BDA0001977431310000132
the information sender Alice and the intermediate node respectively perform joint Bell-based measurement on the two particles owned by the information sender Alice, sixteen measurement results may be obtained, and correspondingly, the particles 4 may collapse to different quantum states. The quantum states to which the particles 4 collapsed corresponding to the sixteen measurements are given in table 1:
table 1: the collapse state of the particle 4 corresponding to the Bell measurement results of Alice and the intermediate node
Figure BDA0001977431310000133
And step 3: and (5) information transmission. And the information sender Alice and the intermediate node respectively send the quantum bit error information and the Bell measurement result of the information sender Alice and the intermediate node to the information receiver Bob.
And 4, step 4: and (4) dislocation correction and information recovery.First, based on the qubit error information of the information sender Alice and the intermediate node, Bob can obtain the matrix U1＝XZ·X,U2Z.Z, thereby determining the error correction matrix as Ucor＝U2U1(ZZ) · (XZX). Secondly, combining the Bell measurement results of all nodes, the quantum invisible state transfer system has the following form:
Figure BDA0001977431310000134
wherein the content of the first and second substances,
Figure BDA0001977431310000141
regardless of the global phase of the quantum state, the information receiver Bob performs a matrix operation U on the particles 4 it holdsrecI.e. the transmitted unknown quantum state information, matrix U, can be recoveredrecIn the form of:
Figure BDA0001977431310000142
the above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (1)

1. A multi-hop quantum invisible state transfer method based on channel error correction is characterized by comprising the following steps:
(1) communication channel construction: the two communication parties are an information sender Alice and an information receiver Bob, and the particle src carries an unknown quantum state | χ>src＝a|0>+b|1>The information sender Alice holds the unknown single-particle quantum state and wants to send the unknown single-particle quantum state to the receiver Bob; the sender Alice holds a particle src and a particle 1, the 1 st intermediate node holds a particle 2 and a particle 3, the 2 nd intermediate node holds a particle 4 and a particle 5, …, and the i (i ═ 1,2,3, …, N) th intermediate node holdsThere are particles 2i and particles 2i +1, where N is a positive integer; a receiver Bob at the target node holds particles 2N + 2; every two adjacent nodes share the same two-bit Bell state quantum channel to form a chain communication channel; the channel form is:
Figure FDA0002287191830000011
due to the interaction between the particles and the surrounding environment, the quantum state may be changed by the influence of quantum noise in the channel transmission process, so as to generate quantum dislocation, and the dislocation information may be one of four types, I, X, Z and XZ; wherein, I-there is no error; the X-bit is anti-error; a Z-phase fault; XZ-bit anti-faulting + bit faulting;
(2) bell measurement: the source node Alice and the N intermediate nodes simultaneously execute combined Bell measurement on two particles owned by the source node Alice and the N intermediate nodes, and four measurement results can be respectively obtained;
(3) information transmission: the source node Alice and the N intermediate nodes simultaneously send dislocation information generated by the particles held by the source node Alice and Bell measurement results of the source node Alice and the N intermediate nodes to a receiver Bob;
(4) dislocation correction, information recovery: bob determines an error correction matrix according to the received error information of all the qubits, and combines the Bell measurement result information of each node to obtain the quantum system with the state:
Figure FDA0002287191830000012
wherein the content of the first and second substances,
Figure FDA0002287191830000021
represents the Bell measurement result of the i (i ═ 1,2, …, N +1) th node;
in the 'communication channel construction' and 'dislocation correction, information recovery', a quantum channel is assumed
Figure FDA0002287191830000022
Entangled particles 2i-1 ofAnd 2i yield qubit errors of: u shapei0,Ui1(i ═ 1,2, …, N +1), and is present
Ui0Ui1＝Ui(i＝1,2,…,N+1)
Wherein, Ui0,Ui1All belong to one of four kinds of quantum bit errors of I, X, Z and XZ;
then Bob obtains an error correction matrix according to the received error information of all qubits as follows:
Ucor＝UN+1UN…U1；
in "dislocation correction, information recovery", when i is 1,
Figure FDA0002287191830000023
representing the Bell measurement result of the information sender Alice, wherein the particle 0 is the carrier particle src of the original unknown quantum state to be transmitted;
Figure FDA0002287191830000024
indicates that when the ith (i-1, 2, …, N +1) node measures the own particles 2i-2 and 2i-1
Figure FDA0002287191830000025
Then, Bob needs to perform on the particle 2N +2 held by Bob
Figure FDA0002287191830000026
A matrix transformation operation;
Figure FDA0002287191830000027
is of the matrix form:
Figure FDA0002287191830000028
regardless of the global phase of the quantum state, the information receiver Bob performs a matrix operation on the particle 2N +2 it holds
Figure FDA0002287191830000029
I.e. the transmitted unknown quantum state information can be recovered.
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