CN111510289A - Bidirectional single-bit state preparation method based on Brown state and network coding - Google Patents

Bidirectional single-bit state preparation method based on Brown state and network coding Download PDF

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CN111510289A
CN111510289A CN202010291203.6A CN202010291203A CN111510289A CN 111510289 A CN111510289 A CN 111510289A CN 202010291203 A CN202010291203 A CN 202010291203A CN 111510289 A CN111510289 A CN 111510289A
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CN111510289B (en
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姜敏
杨甬
陈虹
张佳慧
刘芹
许智航
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Suzhou University
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    • 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
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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
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Abstract

The invention discloses a bidirectional single-bit state preparation method based on Brown state and network coding. The invention combines the state preparation based on the Brown state with the network coding for the first time, carries out cross transmission from a sender to a receiver through the butterfly network and the five-bit Brown state, and prepares the scheme of any single-bit quantum state in a bidirectional way, and is mainly characterized in that: on the basis of a butterfly network coding protocol, a quantum network coding model is established through state preparation. The channel shared by the source node and the destination node is obtained by adding auxiliary particles to a five-bit Brown state and performing channel modulation through a CNOT operation. The method realizes the transmission of the known information in the whole network model, has less resource consumption compared with a quantum invisible transmission scheme, simultaneously achieves higher transmission efficiency, innovatively realizes bidirectional preparation, and has four-bit communication capacity per round. The method has wide application prospect in the technical field of quantum communication networks.

Description

Bidirectional single-bit state preparation method based on Brown state and network coding
Technical Field
The invention relates to the field of quantum communication, in particular to a bidirectional single-bit state preparation method based on Brown state and network coding.
Background
In 2000, Ahlswede et al found a new way in the basic article of Network coding (Network coding) to achieve better Network communication performance than before. The main idea of network coding is that we can encode information at intermediate nodes in the network, thereby improving throughput, and security and reducing the complexity of the network. With the development of quantum information, network coding has been increasingly applied to quantum networks. Quantum Network Coding (QNC) is becoming a major area of research by virtue of its ability to improve the security and efficiency of quantum communications. Hayashi et al explored the possibility of quantum network coding since 2006 and proposed the first quantum network coding protocol XQQ. By designing XQQ protocols, they show that one can design a quantum network coding protocol that can transport a protocol with fidelity greater than 1/2 for a butterfly network across two qubits, and also compute an upper fidelity limit of less than 1.
Based on Hayashi et al work, Iwama initiated a study of quantum network coding for butterfly networks, which demonstrated the feasibility of quantum network coding where approximations were allowed Ma et al [4] proposed a quantum network coding protocol that can transmit M-qudit over butterfly networks by sharing a non-maximally entangled state between the two butterfly networks L eung et al studied the k-pair communication problem of quantum information in quantum channel networks.
The most common application of the concept based on quantum network coding is the combination with the invisible transport state (QT), while the preparation of the known state has been the subject of popular research in the field of quantum communication, and the scheme of state preparation based on Brown state has been proposed in recent years, but there are few concepts based on quantum network coding to achieve the same goal, quantum Remote State Preparation (RSP) and invisible transport state, which are all aimed at delivering one goal to a remote place. However, in quantum remote state preparation, the sender usually knows the state to be transmitted, while in quantum invisible state the sender does not know the state to be transmitted. But is essentially a communication activity that also needs to be secured. The state preparation can accurately prepare and transmit the quantum state which is known to be prepared to a destination node by utilizing the high efficiency and the more excellent security of network coding transmission.
Disclosure of Invention
The invention aims to provide a bidirectional single-bit state preparation method based on Brown state and network coding.
In order to solve the above technical problem, the present invention provides a bidirectional single-bit state preparation method based on Brown state and network coding, comprising:
step 1: a butterfly network model is required to be constructed, wherein A and B are source nodes, and an intermediate node is M1And M2And C and D are used as destination nodes to realize cross two-way state preparation, and any single-bit state is prepared:
destination node C prepares the destination state as
Figure BDA0002450456880000021
Destination node D prepares the destination state as
Figure BDA0002450456880000022
The source node A prepares the target state as
Figure BDA0002450456880000023
The source node B prepares the target state as
Figure BDA0002450456880000024
The source node A and the destination node C share a five-bit Brown state as a channel in advance, and the form of the five-bit Brown state is as follows:
Figure BDA0002450456880000031
the source node B and the destination node D share a five-bit Brown state as a channel in advance, and the form of the five-bit Brown state is as follows:
Figure BDA0002450456880000032
firstly, adding auxiliary particle |00 > to a five-bit Brown state channel shared by a source node A and a destination node C, wherein A1And C1Respectively to the particles A3And C3Channel modulation using CNOT operation, where node A owns particle A1,A2,A3Node C has particle C1,C2,C3. The source node B and the destination node D share a five-bit Brown channel for similar operation to perform channel modulation, wherein the node B has a particle B1,B2,B3Node D having particle D1,D2,D3The two shared channels are respectively in the following two forms:
Figure BDA0002450456880000033
Figure BDA0002450456880000034
step 2: first, a source node A pairs a particle A1Carrying out first amplitude measurement, and selecting a group of orthogonal measurement bases { | mum>,m∈{0,1}}:
Figure BDA0002450456880000035
Then, the particle A is firstly paired according to the source node A1The source node A to the particle A3Performing a second phase measurement, selecting a suitable phase measurement basis (matching according to a coefficient m)
Figure BDA0002450456880000036
Figure BDA0002450456880000037
Figure BDA0002450456880000041
The destination node C is respectively corresponding to the particle pair C1And C3To perform amplitude and phase measurements, a set of orthogonal measurement bases { | η is first takenm>,m∈{0,1}}：
Figure BDA0002450456880000042
Then, the particle C is first paired according to the destination node C1From the measurement basis
Figure BDA0002450456880000043
Selecting corresponding measurement basis (according to m matching) for the particle C3And (3) carrying out phase measurement:
Figure BDA0002450456880000044
Figure BDA0002450456880000045
thus, the overall system of source node a to destination node C can be represented as:
Figure BDA0002450456880000046
in the source node B and the destination node D, first, the source node B pairs the particle B1Carrying out the first amplitude measurement, selecting a group of orthogonal measurement bases { |% χm>,m∈{0,1}}：
Figure BDA0002450456880000047
Then, the first time for the particle B according to the source node B1From the measurement basis
Figure BDA0002450456880000051
Selecting proper phase measurement base (matched according to coefficient m) for the particle B3A second phase measurement is performed:
Figure BDA0002450456880000052
Figure BDA0002450456880000053
for the destination node D, respectively for the particle pairs D1And D3Performing amplitude and phase measurement, firstly selecting a group of orthogonal measurement bases { | v by a destination node Dm>,m∈{0,1}}：
Figure BDA0002450456880000054
Then, the particle D is first paired according to the destination node D1From the measurement basis
Figure BDA0002450456880000055
Selecting corresponding measurement basis (according to m matching) to pair of particles D3A second phase measurement is performed:
Figure BDA0002450456880000056
Figure BDA0002450456880000057
thus, the overall system from source node B to destination node D can be represented as:
Figure BDA0002450456880000058
and step 3: if the controller agrees to state preparation between source node A and destination node C, then the controller performs { |0 for particle E in the opponent>，|1>The measurement result of the control bit E is published to a source node A and a destination node C, and the source node A and the destination node C respectively correspond the respective measurement result to classical information X1，Y1From tables 1 and 2, the measurement results and the classical information X can be seen1，Y1Each via a classical channel Q1，T3To the intermediate node M1And M2The source node A and the destination node C simultaneously send X1，Y1As an auxiliary message, via the classical channel Q2，T4And sending the data to a destination node D and a source node B.
Meanwhile, if the controller agrees to the state preparation between the source node B and the destination node D, the controller performs { |0 on the particle F in the opponent>，|1>The measurement results of the control bit F are published to a source node B and a destination node D, and the source node B and the destination node D respectively correspond the respective measurement results to classical information X2，Y2From tables 3 and 4, the measurement results and the classical information X can be seen2，Y2Each via a classical channel Q3，T1To the intermediate node M1And M2At the same time, the source node B and the destination node D will be X2，Y2As an auxiliary message, via the classical channel Q4，T2And sending the data to a destination node C and a source node A.
And 4, step 4: intermediate node M1From classical channel Q1And Q3Receiving precoding information X separately1And X2And then the received precoding information is subjected to coding processing operation:
Figure BDA0002450456880000061
then utilizes the classical channel Q5To the intermediate node M2And finally the intermediate node M2The received coding processing operations are respectively passed throughChannel Q6And Q7To destination nodes C and D. At the same time, the intermediate node M2From classical channel T1And T3Receiving precoding information Y2And Y1And then the received precoding information is subjected to coding processing operation:
Figure BDA0002450456880000062
then using the classical channel T5To the intermediate node M1And finally the intermediate node M1Passing the received encoding processing operations through the classical channel T respectively6And T7To the source nodes a and B.
And 5: destination nodes C and D pass through classical channel Q according to source nodes B and A4And Q2Transmitted auxiliary information X2And X1Then according to the intermediate node M2Through the classical channel Q6And Q7Transmitted encapsulation information
Figure BDA0002450456880000071
Decoding operation is carried out and control information is combined, the corresponding relation between the measurement result and the classical information can be known through tables 1 and 3, and the | tau can be accurately prepared by adopting corresponding unitary operation1>And | τ2>. Similarly, source nodes A and B pass through classical channel T according to destination nodes D and C2And T4Transmitted auxiliary information Y2And Y1Then according to the intermediate node M1From classical channel T6And T7Transmitted encapsulation information
Figure BDA0002450456880000072
Decoding operation is carried out, control information is combined, the corresponding relation between the measurement result and the classical information can be known through tables 2 and 4, and the | tau can be accurately prepared by adopting corresponding unitary operation3>And | τ4>。
The invention has the beneficial effects that:
based on the combination of five-bit Bown state sum and known quantum information preparation and network coding, the transmission of the known information in the whole network model is realized, compared with a quantum invisible state transmission scheme, the resource consumption is less, the transmission efficiency reaches a higher level, the bidirectional preparation is realized innovatively, and the method has a wide application prospect in the technical field of quantum communication networks.
Based on the same inventive concept, the present application also provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of any of the methods when executing the program.
Based on the same inventive concept, the present application also provides a computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of any of the methods.
Based on the same inventive concept, the present application further provides a processor for executing a program, wherein the program executes to perform any one of the methods.
Drawings
FIG. 1 is a flow chart of the bidirectional preparation arbitrary single-bit quantum network coding method of the present invention.
Fig. 2 is a schematic diagram of the encoding method for bidirectionally preparing any single-bit quantum network.
The symbols in the figures are as follows:
a and B are source nodes of the butterfly network model;
M1and M2Is an intermediate node of the butterfly network model;
c and D are destination nodes of the butterfly network model;
|τm>m ═ 1,2, 3,4 are the known quantum states to be prepared for source nodes a and B and destination nodes C and D, respectively;
Qii ∈ (1,.., 7) is a quantum channel that transmits information when a state is prepared;
Tii ∈ (1.. 7.) is a quantum channel that transfers information from a destination node to a source node;
X1and X2Respectively corresponding classical information of the measurement results of the source node A and the source node B;
Y1and Y2Respectively obtaining classical information corresponding to the measurement results of the target nodes C and D;
Figure BDA0002450456880000081
is an encoding operation;
the dotted line refers to the classical channel;
u is the unitary transformation operation required for the measurement result to correspond to classical information.
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.
Step 1: first, a butterfly network model needs to be constructed, as shown in fig. 2. Wherein, A and B are source nodes, and the intermediate node is M1And M2C and D are used as destination nodes to realize the preparation of the crossed two-way state of A → C, B → D, C → a, D → B, and prepare any single-bit state:
Figure BDA0002450456880000082
Figure BDA0002450456880000083
Figure BDA0002450456880000091
Figure BDA0002450456880000092
the source node A and the destination node C share a five-bit Brown state as a channel in advance, and the form of the five-bit Brown state is as follows:
Figure BDA0002450456880000093
the source node B and the destination node D share a five-bit Brown state as a channel in advance, and the form of the five-bit Brown state is as follows:
Figure BDA0002450456880000094
firstly, adding auxiliary particles into a five-bit Brown channel shared by a source node A and a destination node C
Figure BDA0002450456880000095
Wherein A is1And C1Respectively to the particles A3And C3The CNOT operation is performed and the channel changes to the following form:
Figure BDA0002450456880000096
wherein node A possesses particle A1,A2,A3Node C has particle C1,C2,C3。
The source node B operates similarly to the five bit Brown state channel shared by the destination node D, which changes to the following form:
Figure BDA0002450456880000097
wherein node B has a particle B1,B2,B3Node D having particle D1,D2,D3。
Step 2: in the source node A and the destination node C, first, the source node A pairs the particle A1Carrying out first amplitude measurement, and selecting a group of orthogonal measurement bases { | mum>,m∈{0,1}}：
Figure BDA0002450456880000101
Then, the particle A is firstly paired according to the source node A1The source node A to the particle A3Performing a second phase measurementSelecting proper phase measuring base (according to the matching of the coefficient m, the measuring bases with the same coefficient m are matched)
Figure BDA0002450456880000102
When m is 0, the source node A is opposite to the particle A1The measurement basis chosen for the first amplitude measurement is | μ0>Source node A to particle A3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000103
when m is 1, the source node A is opposite to the particle A1The measurement basis chosen for the first amplitude measurement is | μ1>Source node A to particle A3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000104
for the destination node C, respectively for the particle pair C1And C3To perform amplitude and phase measurements, a set of orthogonal measurement bases { | η is first takenm>,m∈{0,1}}：
Figure BDA0002450456880000105
Then, the particle C is first paired according to the destination node C1From the measurement basis
Figure BDA0002450456880000106
Selecting corresponding measuring bases (matching according to the coefficient m, matching the measuring bases with the same coefficient m) to the particles C3And (3) carrying out phase measurement:
when m is 0, the destination node C is opposite to the particle C1The measurement basis chosen for the first amplitude measurement is | η0>Destination node C to particle C3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000111
when m is 1, the destination node C is opposite to the particle C1The measurement basis chosen for the first amplitude measurement is | η1>Destination node C to particle C3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000112
thus, the overall system of source node a to destination node C can be represented as:
Figure BDA0002450456880000113
TABLE 1 results of two measurements of Source node A, particle C2Unitary operation with classical information X1In relation to (2)
Figure BDA0002450456880000114
TABLE 2 results of two measurements of destination point C, particle A2Is unitary with the classical information Y1In relation to (2)
Figure BDA0002450456880000115
Figure BDA0002450456880000121
In the source node B and the destination node D, first, the source node B pairs the particle B1Carrying out the first amplitude measurement, selecting a group of orthogonal measurement bases { |% χm>,m∈{0,1}}：
Figure BDA0002450456880000122
Then, according to the source node B, the firstSecondary pair of particles B1From the measurement basis
Figure BDA0002450456880000123
Selecting proper phase measurement bases (matching according to coefficient m, matching measurement bases with the same coefficient m) to the particles B3A second phase measurement is performed:
when m is 0, the source node B is opposite to the particle B1The measurement basis chosen for the first amplitude measurement is | χ0>Source node B to particle B3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000124
when m is 1, the source node B is opposite to the particle B1The measurement basis chosen for the first amplitude measurement is | χ1>Source node B to particle B3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000125
for the destination node D, respectively for the particle pairs D1And D3Performing amplitude and phase measurement, firstly selecting a group of orthogonal measurement bases { | v by a destination node Dm>,m∈{0,1}}：
Figure BDA0002450456880000131
Then, the particle D is first paired according to the destination node D1From the measurement basis
Figure BDA0002450456880000132
Selecting corresponding measuring base (matching according to coefficient m, matching measuring base with same coefficient m) particles D3A second phase measurement is performed:
when m is 0, the destination node D is opposite to the particle D1The measurement basis chosen for the first amplitude measurement is | v0>Destination node D to particle D3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000133
when m is 1, the destination node D is opposite to the particle D1The measurement basis chosen for the first amplitude measurement is | v1>Destination node D to particle D3The measurement bases selected for the second phase measurement are:
Figure BDA0002450456880000134
thus, the overall system from source node B to destination node D can be represented as:
Figure BDA0002450456880000135
TABLE 3 results of two measurements of Source node B, particle D2Unitary operation with classical information X2In relation to (2)
Figure BDA0002450456880000136
Figure BDA0002450456880000141
TABLE 4 results of two measurements of destination Point D, particle B2Is unitary with the classical information Y2In relation to (2)
Figure BDA0002450456880000142
And step 3: if the controller agrees to state preparation between source node A and destination node C, then the controller performs { |0 for particle E in the opponent>，|1>The measurement result of the control bit E is published to the source node A and the destination node C, and then the source node A and the destination node C respectively measure the respective measurement resultsThe result pair becomes classical information X1，Y1From tables 1 and 2, the measurement results and the classical information X can be seen1，Y1Each via a classical channel Q1，T3To the intermediate node M1And M2The source node A and the destination node C simultaneously send X1，Y1As an auxiliary message, via the classical channel Q2，T4And sending the data to a destination node D and a source node B.
Meanwhile, if the controller agrees to the state preparation between the source node B and the destination node D, the controller performs { |0 on the particle F in the opponent>，|1>The measurement results of the control bit F are published to the source node B and the destination node D, and then the source node B and the destination node D respectively correspond the respective measurement results to classical information X2，Y2From tables 3 and 4, the measurement results and the classical information X can be seen2，Y2Each via a classical channel Q3，T1To the intermediate node M1And M2At the same time, the source node B and the destination node D will be X2，Y2As an auxiliary message, via the classical channel Q4，T2And sending the data to a destination node C and a source node A.
And 4, step 4: thus, the intermediate node M1From classical channel Q1And Q3Receiving precoding information X1And X2And then the received precoding information is subjected to coding processing operation:
Figure BDA0002450456880000151
then utilizes the classical channel Q5To the intermediate node M2And finally the intermediate node M2Passing the received encoding processing operations through the classical channel Q6And Q7To destination nodes C and D.
At the same time, the intermediate node M2From classical channel T1And T3Receiving precoding information Y2And Y1And then the received precoding information is subjected to coding processing operation:
Figure BDA0002450456880000152
then using the classical channel T5To the intermediate node M1And finally the intermediate node M1Passing the received encoding processing operations through the classical channel T respectively6And T7To the destination nodes a and B.
And 5: the destination nodes C and D transmit the auxiliary information X via the classical channel according to the source nodes B and A2And X1Then according to the intermediate node M2Through the classical channel Q6And Q7Transmitted encapsulation information
Figure BDA0002450456880000153
Performing decoding operation to recover X1And X2The correspondence between the measurement results and the classical information and the particle unitary operation can be seen from tables 1 and 3. X1And X2May be 00/01/10/11, based on the measurement |0 of the particles E and F in the control party's opponent>/| 1>, the corresponding unitary operation U can be found from tables 1 and 30/U1/U2/U3. According to the corresponding unitary operation found, the target nodes C and D respectively adopt the corresponding unitary operation, and the target nodes C and D can accurately and unmistakably prepare the | tau1>And | τ2>. Similarly, the source nodes A and B transmit the auxiliary information Y over the classical channel according to the destination nodes D and C2And Y1Then according to the intermediate node M1From classical channel T6And T7Transmitted encapsulation information
Figure BDA0002450456880000154
Performing decoding operation to obtain Y1And Y2And in combination with the control information, the correspondence of the measurement results to the classical information and the particle unitary operation can be seen from tables 2 and 4. Y is1And Y2May be 00/01/10/11, based on the measurement |0 of the particles E and F in the control party's opponent>/|1>Through tables 2 and 4, the corresponding unitary operation U can be found0/U1/U2/U3. According to the found pairsThe source nodes A and B respectively adopt corresponding unitary operation, and the destination nodes A and B can accurately and unmistakably prepare the | tau3>And | τ4>。
The first embodiment is as follows: preparing a target state as
Figure BDA0002450456880000161
Destination node D prepares the destination state as
Figure BDA0002450456880000162
The source node A prepares the target state as
Figure BDA0002450456880000163
The source node B prepares the target state as
Figure BDA0002450456880000164
For example, the specific steps are as follows:
step 1: the source node A and the destination node C share a five-bit Brown state as a channel in advance, and the form of the five-bit Brown state is as follows:
Figure BDA0002450456880000165
the source node B and the destination node D share a five-bit Brown state as a channel in advance, and the form of the five-bit Brown state is as follows:
Figure BDA0002450456880000166
firstly, adding auxiliary particles into a five-bit Brown channel shared by a source node A and a destination node C
Figure BDA0002450456880000167
Wherein A is1And C1Respectively to the particles A3And C3The CNOT operation is performed and the channel changes to the following form:
Figure BDA0002450456880000168
wherein node A possesses particle A1,A2,A3Node C has particle C1,C2,C3。
The source node B operates similarly to the five bit Brown state channel shared by the destination node D, which changes to the following form:
Figure BDA0002450456880000171
wherein node B has a particle B1,B2,B3Node D having particle D1,D2,D3。
Step 2: in the source node A and the destination node C, first, the source node A pairs the particle A1Carrying out first amplitude measurement, and selecting a group of orthogonal measurement bases { | mum>,m∈{0,1}}：
Figure BDA0002450456880000172
First pairing particles A according to source node A1The source node A to the particle A3Performing a second phase measurement, selecting a suitable phase measurement basis (matching according to coefficient m, matching measurement bases with the same coefficient m)
Figure BDA0002450456880000173
Figure BDA0002450456880000174
Figure BDA0002450456880000175
The destination node C is respectively corresponding to the particle pair C1And C3Performing amplitude and phase measurements by first selecting a set of orthogonal measurements by the destination node CRadical { | ηm>,m∈{0,1}}：
Figure BDA0002450456880000176
First pairing particles C according to destination node C1Selecting corresponding measurement bases (matching according to coefficient m, matching measurement bases with the same coefficient m) to the particles C according to the amplitude measurement result of the particles C3Performing phase measurements
Figure BDA0002450456880000181
Figure BDA0002450456880000182
Figure BDA0002450456880000183
Thus, the overall system of source node a to destination node C can be represented as:
Figure BDA0002450456880000184
in the source node B and the destination node D, first, the source node B pairs the particle B1Carrying out the first amplitude measurement, selecting a group of orthogonal measurement bases { |% χm>,m∈{0,1}}：
Figure BDA0002450456880000185
Then, the first time for the particle B according to the source node B1The source node A to the particle B3Performing a second phase measurement, selecting a suitable phase measurement basis (matching according to coefficient m, matching measurement bases with the same coefficient m)
Figure BDA0002450456880000186
Figure BDA0002450456880000187
Figure BDA0002450456880000191
Destination node D is respectively corresponding to particle pair D1And D3Performing amplitude and phase measurement, firstly selecting a group of orthogonal measurement bases { | v by a destination node Dm>,m∈{0,1}}：
Figure BDA0002450456880000192
First pairing particles D according to destination node D1Selecting corresponding measurement bases (matching according to coefficient m, matching measurement bases with the same coefficient m) to the particles D according to the amplitude measurement result of the particles D3Performing phase measurements
Figure BDA0002450456880000193
Figure BDA0002450456880000194
Figure BDA0002450456880000195
Thus, the overall system from source node B to destination node D can be represented as:
Figure BDA0002450456880000196
and step 3: if the controller agrees to state preparation between source node A and destination node C, then the controller performs { |0 for particle E in the opponent>，|1>H, measurement of control bit E |0>The measurement result is published to a source node A and a destination node C, and the source node A and the destination node C respectively correspond the respective measurement result to classical information X1，Y1From tables 1 and 2, the measurement results and the classical information X can be seen1，Y1Obtaining the corresponding relation ofTo classical information X1＝10，Y100, each over a classical channel Q1，T3To the intermediate node M1And M2The source node A and the destination node C simultaneously send X1，Y1As an auxiliary message, via the classical channel Q2，T4And sending the data to a destination node D and a source node B.
Meanwhile, if the controller agrees to the state preparation between the source node B and the destination node D, the controller performs { |0 on the particle F in the opponent>，|1>Will measure |1 of the control bit F>The measurement result is published to a source node B and a destination node D, and the source node B and the destination node D respectively correspond the respective measurement result to classical information X2，Y2From tables 3 and 4, the measurement results and the classical information X can be seen2，Y2Obtaining the classical information as X2＝01，Y201, each over a classical channel Q3，T1To the intermediate node M1And M2At the same time, the source node B and the destination node D will be X2，Y2As an auxiliary message, via the classical channel Q4，T2And sending the data to a destination node C and a source node A.
And 4, step 4: thus, the intermediate node M1From classical channel Q1And Q3Receiving the pre-coding information, and then performing coding processing operation on the received pre-coding information:
Figure BDA0002450456880000201
then utilizes the classical channel Q5To a second intermediate node M2And finally the intermediate node M2Passing the received encoding processing operations through the classical channel Q6And Q7To destination nodes C and D.
At the same time, the intermediate node M2From classical channel T1And T3Receiving the pre-coding information, and then performing coding processing operation on the received pre-coding information:
Figure BDA0002450456880000202
then using the classical channel T5To a second intermediate node M1And finally the intermediate node M1Passing the received encoding processing operations through the classical channel T respectively6And T7To source nodes a and B.
And 5: the destination nodes C and D transmit the auxiliary information X via the classical channel according to the source nodes B and A201 and X110, and then according to the intermediate node M2Through the classical channel Q6And Q7Transmitted encapsulation information
Figure BDA0002450456880000203
Performing decoding operation to recover X110 and X201, and the corresponding relation between the measurement result and the classical information and the particle unitary operation can be known through tables 1 and 3 in combination with the control information, and the unitary operation U is respectively adopted3And U0The destination nodes C and D can be respectively and accurately prepared:
Figure BDA0002450456880000211
similarly, the source nodes A and B transmit the auxiliary information Y over the classical channel according to the destination nodes D and C201 and Y100, and then according to the intermediate node M1From classical channel T6And T7Transmitted encapsulation information
Figure BDA0002450456880000212
Performing decoding operation to obtain Y100 and Y2The corresponding relation between the measurement result and the classical information and the particle unitary operation can be known through tables 2 and 4 by combining the value of 01 and the control information, and the unitary operation U is respectively adopted0And U0The destination nodes A and B can be respectively and accurately prepared as follows:
Figure BDA0002450456880000213
in addition, there are three cases, which are: the measurement nodes of the control party for the control bits E and F are respectively |0>, |0>, the measurement nodes of the control party for the control bits E and F are respectively |1>, |0>, and the measurement nodes of the control party for the control bits E and F are respectively |1>, |1 >; the whole process is similar to the above process, and is not repeated here.
The source node and the destination node in each communication process can prepare two single bits by utilizing, so that the capacity of each round of the whole preparation scheme based on network coding is four bits, and the functions of a channel, particularly an intermediate node, are greatly utilized.
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 (10)

1. A method for preparing a bidirectional single bit state based on a Brown state and network coding is characterized by comprising the following steps:
step 1: a butterfly network model is required to be constructed, wherein A and B are source nodes, and an intermediate node is M1And M2And C and D are used as destination nodes to realize cross two-way state preparation, and any single-bit state is prepared:
destination node C prepares the destination state as
Figure FDA0002450456870000011
Destination node D prepares the destination state as
Figure FDA0002450456870000012
The source node A prepares the target state as
Figure FDA0002450456870000013
The source node B prepares the target state as
Figure FDA0002450456870000014
The source node A and the destination node C share a five-bit Brown state as a channel in advance;
the source node B and the destination node D share a five-bit Brown state as a channel in advance;
firstly, adding auxiliary particle |00 into a five-bit Brown state channel shared by a source node A and a destination node C>Wherein A is1And C1Respectively to the particles A3And C3Channel modulation using CNOT operation, where node A owns particle A1,A2,A3Node C has particle C1,C2,C3(ii) a The source node B and the destination node D share a five-bit Brown channel for similar operation to perform channel modulation, wherein the node B has a particle B1,B2,B3Node D having particle D1,D2,D3；
Step 2: first, a source node A pairs a particle A1Carrying out first amplitude measurement, and selecting a group of orthogonal measurement bases { | mum>,m∈{0,1}}:
Figure FDA0002450456870000015
Then, the particle A is firstly paired according to the source node A1The source node A to the particle A3Performing a second phase measurement, and selecting a suitable phase measurement basis
Figure FDA0002450456870000016
Figure FDA0002450456870000021
Figure FDA0002450456870000022
The destination node C is respectively corresponding to the particle pair C1And C3Amplitude of executionAnd phase measurement, preferably a set of orthogonal measurement bases { | ηm>,m∈{0,1}}：
Figure FDA0002450456870000023
Then, the particle C is first paired according to the destination node C1From the measurement basis
Figure FDA0002450456870000024
Selecting corresponding measurement base pair particles C3And (3) carrying out phase measurement:
Figure FDA0002450456870000025
Figure FDA0002450456870000026
in the source node B and the destination node D, first, the source node B pairs the particle B1Carrying out the first amplitude measurement, selecting a group of orthogonal measurement bases { |% χm>,m∈{0,1}}：
Figure FDA0002450456870000027
Then, the first time for the particle B according to the source node B1From the measurement basis
Figure FDA0002450456870000028
Selecting proper phase measurement base pair particle B3A second phase measurement is performed:
Figure FDA0002450456870000029
Figure FDA0002450456870000031
for the destination node D, respectively for the particle pairs D1And D3Performing amplitude and phase measurement, firstly selecting a group of orthogonal measurement bases { | v by a destination node Dm>,m∈{0,1}}：
Figure FDA0002450456870000032
Then, the particle D is first paired according to the destination node D1From the measurement basis
Figure FDA0002450456870000033
Selecting corresponding measurement base pair particles D3A second phase measurement is performed:
Figure FDA0002450456870000034
Figure FDA0002450456870000035
and step 3: if the controller agrees to state preparation between source node A and destination node C, then the controller performs { |0 for particle E in the opponent>，|1>The measurement result of the control bit E is published to a source node A and a destination node C, and the source node A and the destination node C respectively correspond the respective measurement result to classical information X1，Y1From tables 1 and 2, the measurement results and the classical information X can be seen1，Y1Each via a classical channel Q1，T3To the intermediate node M1And M2The source node A and the destination node C simultaneously send X1，Y1As an auxiliary message, via the classical channel Q2，T4Sending the data to a destination node D and a source node B;
meanwhile, if the controller agrees to the state preparation between the source node B and the destination node D, the controller performs { |0 on the particle F in the opponent>，|1>Will disclose the measurement result for the control bit FDistributed to a source node B and a destination node D, which respectively correspond respective measurement results to classical information X2，Y2From tables 3 and 4, the measurement results and the classical information X can be seen2，Y2Each via a classical channel Q3，T1To the intermediate node M1And M2At the same time, the source node B and the destination node D will be X2，Y2As an auxiliary message, via the classical channel Q4，T2Sending the data to a destination node C and a source node A;
and 4, step 4: intermediate node M1From classical channel Q1And Q3Receiving precoding information X separately1And X2And then the received precoding information is subjected to coding processing operation:
Figure FDA0002450456870000041
then utilizes the classical channel Q5To the intermediate node M2And finally the intermediate node M2Passing the received encoding processing operations through the classical channel Q6And Q7Transmitting to destination nodes C and D; at the same time, the intermediate node M2From classical channel T1And T3Receiving precoding information Y2And Y1And then the received precoding information is subjected to coding processing operation:
Figure FDA0002450456870000042
then using the classical channel T5To the intermediate node M1And finally the intermediate node M1Passing the received encoding processing operations through the classical channel T respectively6And T7Transmitting the data to source nodes A and B;
and 5: destination nodes C and D pass through classical channel Q according to source nodes B and A4And Q2Transmitted auxiliary information X2And X1Then according to the intermediate node M2Through the classical channel Q6And Q7Transmitted encapsulation information
Figure FDA0002450456870000043
Decoding operation is carried out and control information is combined, the corresponding relation between the measurement result and the classical information can be known through tables 1 and 3, and the | tau can be accurately prepared by adopting corresponding unitary operation1>And | τ2>(ii) a Similarly, source nodes A and B pass through classical channel T according to destination nodes D and C2And T4Transmitted auxiliary information Y2And Y1Then according to the intermediate node M1From classical channel T6And T7Transmitted encapsulation information
Figure FDA0002450456870000044
Decoding operation is carried out, control information is combined, the corresponding relation between the measurement result and the classical information can be known through tables 2 and 4, and the | tau can be accurately prepared by adopting corresponding unitary operation3>And | τ4>。
2. The method for bi-directional single-bit state preparation based on Brown state and network coding of claim 1, wherein the form of the five-bit Brown state pre-shared by the source node a and the destination node C is as follows:
Figure FDA0002450456870000045
3. the method for bi-directional single-bit state preparation based on Brown state and network coding of claim 1, wherein the form of the five-bit Brown state pre-shared by the source node B and the destination node D is as follows:
Figure FDA0002450456870000051
4. the Brown state and network coding based bi-directional single-bit state preparation method of claim 1, wherein the source node a and the destination node C share a five-bit Brown state channel form as follows:
Figure FDA0002450456870000052
5. the Brown state and network coding based bi-directional single-bit state preparation method of claim 1, wherein the source node B and the destination node D share a five-bit Brown state channel form as follows:
Figure FDA0002450456870000053
6. the method for bi-directional single-bit state preparation based on Brown state and network coding of claim 1, wherein in step 2, the whole system from the source node a to the destination node C can be expressed as:
Figure FDA0002450456870000054
7. the method for bi-directional single-bit state preparation based on Brown state and network coding of claim 1, wherein in step 2, the whole system from the source node B to the destination node D can be expressed as:
Figure FDA0002450456870000061
8. a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method of any of claims 1 to 7 are implemented when the program is executed by the processor.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
10. A processor, characterized in that the processor is configured to run a program, wherein the program when running performs the method of any of claims 1 to 7.
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