Measurement equipment-independent quantum secure direct communication method based on quantum walking

Abstract

The invention discloses a quantum walking-based measurement equipment-independent quantum secure direct communication method. The method comprises the steps of encoding a position state in a position space and a coin state in a hardware space; obtaining a shared entangled state used as a quantum channel based on quantum walking on a straight line; the shared quantum channel is described and measured again; detecting the quantum channel and judging the security of the quantum channel; the sending end and the receiving end carry out measurement and entanglement through a third party; the sending end and the receiving end confirm the security of the quantum channel again; combining the particles of the sending end and the receiving end to obtain a composite quantum state; second-step quantum walking is carried out to obtain quantum entanglement states of the sending end and the receiving end; and the transmitting end performs projection measurement on the quantum entanglement state and transmits a measurement result to the receiving end, so that final quantum secure direct communication irrelevant to the measurement equipment is completed. According to the invention, quantum secure direct communication irrelevant to measurement equipment can be realized, the reliability is high, and the security is good.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum communication, and in particular relates to a measurement device-independent quantum secure direct communication method based on quantum walk. Background Art

[0002] With the development of economy and technology and the improvement of people's living standards, people's demand for information security is getting higher and higher. As an important branch of quantum information science, quantum communication has unconditional communication security under the guarantee of three basic principles (i.e., the inherent uncertainty of quantum mechanics, measurement collapse and non-cloning), so it has also attracted more and more attention.

[0003] As the core technology of quantum communication, quantum key distribution (QKD) has been extensively studied in both theory and experiment. Quantum key distribution allows the parties to transmit messages by sharing secure random keys without being restricted by physical distance. At the same time, as another important component of quantum communication, quantum secure direct communication (QSDC) allows the communicating parties to directly transmit secret messages on the quantum channel without providing pre-shared keys. In this sense, QSDC can not only save quantum resources, but also avoid potential security risks associated with keys and ciphertexts, thereby reducing the complexity of the communication system.

[0004] The QSDC protocol has a perfect quantum source, a noise-free channel, perfect equipment and detectors, and is completely safe under ideal conditions. However, in the real world, quantum communication systems often have problems with imperfect equipment, especially defects in measurement equipment; these defects may pose potential security threats, such as eavesdroppers may exploit vulnerabilities in these devices to steal information. Therefore, the current QSDC scheme does have problems with low security and poor reliability. Summary of the invention

[0005] The purpose of the present invention is to provide a measurement device-independent quantum secure direct communication method based on quantum walk with high security and good reliability.

[0006] The measurement device-independent quantum secure direct communication method based on quantum walk provided by the present invention comprises the following steps:

[0007] S1. encoding a position state in a position space, and encoding a coin state in a coin space;

[0008] S2. Perform a quantum walk based on a straight line to obtain a shared entangled state used as a quantum channel, completing the preparation of the quantum channel;

[0009] S3. Re-describe and measure the shared quantum channel;

[0010] S4. Detect the quantum channel to determine the security of the quantum channel;

[0011] S5. The transmitter and receiver are measured and entangled by a third party;

[0012] S6. According to the result of step S5, the sending end and the receiving end confirm the security of the quantum channel again;

[0013] S7. Merge the particles at the transmitting end and the receiving end to obtain a composite quantum state;

[0014] S8. Perform a second quantum walk on the obtained composite quantum state to obtain the quantum entangled state of the transmitter and the receiver;

[0015] S9. The sending end performs projection measurement on the quantum entangled state and sends the measurement result to the receiving end, completing the final quantum secure direct communication that is independent of the measurement device.

[0016] The encoding of the position state in the position space and the encoding of the coin state in the coin space described in step S1 specifically include the following steps:

[0017] Consider a measurement device independent (MDI) model based on quantum walk on a straight line. The model includes a position space and a coin space named coin 1. The sender holds particles A1 and A3.

[0018] Encode the position state in the position space onto particle A1, and encode the coin 1 state in the coin 1 space onto particle A3;

[0019] Assume that the initial states prepared by the sender on A1 and A3 are both |0>;

[0020] The initial state of the quantum walk is expressed as in is the tensor product.

[0021] The execution described in step S2 is based on the quantum walk on a straight line, thereby obtaining a shared entangled state used as a quantum channel and completing the preparation of the quantum channel, which specifically includes the following steps:

[0022] By performing a straight-line quantum walk on the quantum state |φ>0, the transmitter obtains a shared entangled state for the quantum channel.

[0023] A quantum walk on a straight line is represented by

[0024]

[0025] Where W1 is the quantum walk operator on the first straight line; E1 is the conditional shift operator; I1 is the unit operator acting on the position space; C1 is the coin operator acting on the coin space 1 at the sending end, which can be any single quantum bit operation such as the unit gate, Hadamard gate, etc., and it is assumed to be an H (Hadamard) gate here; is the tensor product; S is the shift operator; Represents the conjugate transpose (Hermitian conjugation) operator of S, usually used for inverse operation;

[0026] After one step of quantum walk evolution on a straight line, the new quantum state is obtained:

[0027]

[0028] The transmitting end and the receiving end each repeat steps S1 and S2 several times to prepare quantum states that meet the set number, thereby each preparing n pairs of entangled states;

[0029] The transmitter and receiver prepare m coin position super-coded single photons, each of which is randomly in a state of {|0>,|1>,|+>,|->}, where

[0030] The ordered sequence of the first particle formed by the entanglement pair created by quantum walking at the sending end (receiving end) is S A (S B ); the sender (receiver) inserts the single photon into the ordered sequence C consisting of the remaining partner photons of the entangled pair A (C B ) at a random position; at this time, the sequence S A There are n photons, sequence S B There are n photons, sequence C A There are n+m photons, sequence C B There are n+m photons.

[0031] The re-describing and measuring of the quantum channel in step S3 specifically includes the following steps:

[0032] The sending quantum channel |φ>1 is redescribed as a position-based measurement basis {|-1>|0>,|1>,|2>} and a coin-based measurement basis {|+>,|->}, expressed as

[0033]

[0034] Set a subset selected from the entangled state set {|φ>1}; the sender first uses the measurement basis {|-1>|0>,|1>,|2>} to measure particle A1, and after obtaining the measured entangled state, it uses the measurement basis {|+>,|->} to measure another particle corresponding to the entangled state;

[0035] The quantum channel |φ>1 at the receiving end is redescribed as a position-based measurement basis {|-1>|0>,|1>,|2>} and a coin-based measurement basis {|+>,|->}, expressed as

[0036]

[0037] Set a subset selected from the entangled state set {|φ>1}; the receiving end first uses the measurement basis {|-1>|0>,|1>,|2>} to measure particle B1, and after obtaining the measured entangled state, uses the measurement basis {|+>,|->} to measure another particle corresponding to the entangled state.

[0038] The step S4 of detecting the quantum channel to determine the security of the quantum channel specifically includes the following steps:

[0039] The transmitter detects the quantum channel by comparing the measurement result with four possible output results; the measurement output and the corresponding quantum state of the transmitter are

[0040] If the measurement result on A1 is 1 and the measurement result on A3 is 1, then the associated quantum state is |1>|+>;

[0041] If the measurement result on A1 is 1 and the measurement result on A3 is -1, then the associated quantum state is |1>|->;

[0042] The measurement result on A1 is -1 and the measurement result on A3 is 1, then the associated quantum state is |-1>|+>;

[0043] The measurement result on A1 is -1 and the measurement result on A3 is -1, then the associated quantum state is |-1>|->;

[0044] If the comparison error rate of all output results is lower than the set threshold, the sender determines that the quantum channel is secure and proceeds to the subsequent steps;

[0045] Otherwise, the sender determines that there may be a risk of eavesdropping.

[0046] Similarly, the receiving end detects the quantum channel by comparing the measurement result with the four possible output results; the measurement output of the receiving end and the corresponding quantum state are

[0047] If the measurement result on B1 is 1 and the measurement result on B3 is 1, then the associated quantum state is |1>|+>;

[0048] If the measurement result on B1 is 1 and the measurement result on B3 is -1, then the associated quantum state is |1>|->;

[0049] The measurement result on B1 is -1 and the measurement result on B3 is 1, then the associated quantum state is |-1>|+>;

[0050] The measurement result on B1 is -1 and the measurement result on B3 is -1, then the associated quantum state is |-1>|->;

[0051] If the comparison error rate of all output results is lower than the set threshold, the receiving end determines that the quantum channel is secure and proceeds to the subsequent steps;

[0052] Otherwise, the receiving end determines that there may be a risk of eavesdropping.

[0053] The transmitter and receiver described in step S5 are measured and entangled by a third party, which specifically includes the following steps:

[0054] The sender sends sequence C A Send to a third party; the receiving end sends sequence C B Sent to a third party; at the same time, ensure S A At the sending end, S B On the receiving end;

[0055] The third party receives C A and C B conduct Basis measurement, and publish the measurement results; through |φ'> basis measurement, S A and S B The corresponding partner photons will become entangled, and this process is similar to entanglement exchange.

[0056] According to the result of step S5, the transmitting end and the receiving end reconfirm the security of the shared quantum channel in step S6, which specifically includes the following steps:

[0057] The transmitter sends m photons at C A The position of the photons is published, and the receiving end sends m photons to C B The position in the announcement;

[0058] The sender exchanges the information of m photons with the receiver;

[0059] Determination of different photon combinations and corresponding effects, including

[0060] If C A is an entangled photon and C BFor entangled photons, the corresponding effect is the entanglement exchange of message transmission;

[0061] If C A is a single photon and C B If it is a single photon, the corresponding function is safety check;

[0062] If C A is an entangled photon and C B If it is a single photon, there is no corresponding effect;

[0063] If C A is a single photon and C B For entangled photons, there is no corresponding effect;

[0064] By measuring single photons of the same basis, the sender and receiver estimate the error rate, thereby reconfirming the security of the quantum channel.

[0065] The step S7 of merging the particles at the transmitting end and the receiving end to obtain a composite quantum state specifically includes the following steps:

[0066] The sending end introduces a new coin space particle A2, which merges the sending end particles A1 and A2 and the receiving end particle B1, where A1 and B1 are entangled together through the advantage of MDI, and the composite quantum state is obtained as follows:

[0067]

[0068] Where |ψ>0 is the composite quantum state of the communication system of particles A1 and A2 at the sending end and particle B1 at the receiving end; It refers to a specific quantum state formed by quantum entanglement between particle A1 at the sending end and particle B1 at the receiving end in this composite quantum system.

[0069] The second step of quantum walking is performed on the obtained composite quantum state in step S8 to obtain the quantum entangled state of the transmitting end and the receiving end, which specifically includes the following steps:

[0070] Perform the second quantum walk on the quantum state |ψ>0 Where W2 represents the final quantum state after the second quantum walk on the system composite quantum state |ψ>0, E2 represents the evolution operator of the second quantum walk, which describes the evolution process of the quantum state in this walk, and I P represents the unit operator acting on the position space, C2 represents the coin operator acting on the second coin space, here is the I (Identity) gate, and I2 represents the unit operator acting on the second position space;

[0071] Assume that the state of coin 2 on particle A2 is the control state, and the position state on particle A1 is the target state. Then the quantum entangled state obtained by the transmitter and the receiver is

[0072]

[0073] Where |ψ>1 is the entangled state of the quantum system after the second quantum walk.

[0074] The transmitting end in step S9 performs projection measurement on the quantum entangled state and sends the measurement result to the receiving end, thereby completing the final measurement device-independent quantum secure direct communication, which specifically includes the following steps:

[0075] The sender performs projection measurement of particles A2 and A1 on |ψ>1: the sender uses the measurement basis {|+>,|->} to measure A2, and the corresponding measurement output result is recorded as {1,-1}; the sender then uses the measurement basis Measure particle A1, where | And record the corresponding measurement output result as {1,0,-1}; finally, the transmitter sends the measurement result to the receiver;

[0076] In order to transmit quantum states, the measurement results of the transmitter on particles A2 and A1 and the local forward operation of the receiver on particle B1 are related as follows:

[0077] The measurement result of the transmitter on particle A2 is {1,1} and the measurement result on particle A1 is {-1,1}, then the local unitary operation of the receiver on row B1 is I;

[0078] The measurement result of the transmitter on particle A2 is {1,-1} and the measurement result on particle A1 is {-1,-1}, then the local unitary operation of the receiver on row B1 is Z;

[0079] The measurement result of the transmitter on particle A2 is {1} and the measurement result on particle A1 is {0}, then the local unitary operation of the receiver on row B1 is X;

[0080] The measurement result of the transmitter on particle A2 is {-1} and the measurement result on particle A1 is {0}, so the local unitary operation of the receiver on row B1 is ZX;

[0081] Ultimately, quantum secure direct communication that is independent of the measurement device is achieved.

[0082] The measurement device-independent quantum secure direct communication method based on quantum walk provided by the present invention uses a single-step quantum walk to prepare an entangled state and uses a two-step quantum walk to establish a secure quantum channel. Therefore, the present invention can not only realize measurement device-independent quantum secure direct communication, but also has higher reliability and better security. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 The figure is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION

[0084] like Figure 1 The method flow chart of the method of the present invention is shown as follows: The measurement device-independent quantum secure direct communication method based on quantum walk provided by the present invention comprises the following steps:

[0085] Quantum channel preparation phase: This phase aims to prepare the entangled state as a quantum channel that meets the communication needs of sender Alice and receiver Bob;

[0086] S1. Encoding the position state in the position space and encoding the coin state in the coin space; specifically comprising the following steps:

[0087] Consider a measurement device independent (MDI) model based on quantum walk on a straight line. The model includes a position space and a coin space named coin 1. The sender holds particles A1 and A3.

[0088] Encode the position state in the position space onto particle A1, and encode the coin 1 state in the coin 1 space onto particle A3;

[0089] The initial states prepared by the sender on A1 and A3 are both |0>;

[0090] The initial state of the quantum walk is expressed as in is the tensor product;

[0091] S2. Perform a quantum walk based on a straight line to obtain a shared entangled state used as a quantum channel and complete the preparation of the quantum channel; specifically, the steps include:

[0092] By performing a straight-line quantum walk on the quantum state |φ>0, the transmitter obtains a shared entangled state for the quantum channel.

[0093] A quantum walk on a straight line is represented by

[0094]

[0095] Where W1 is the quantum walk operator on the first straight line; E1 is the conditional shift operator; I1 is the unit operator acting on the position space; C1 is the coin operator acting on the coin space 1 at the sending end, which can be any single quantum bit operation such as the unit gate, Hadamard gate, etc., and it is assumed to be an H (Hadamard) gate here; is the tensor product; S is the shift operator; is the conjugate transpose (Hermitian conjugate) operator of S, usually used for inverse operations;

[0096] After one step of quantum walk evolution on a straight line, the new quantum state is obtained:

[0097]

[0098] The transmitting end and the receiving end each repeat steps S1 and S2 several times to prepare quantum states that meet the set number, thereby each preparing n pairs of entangled states;

[0099] In order to prepare for the subsequent detection channel and entangled state preparation stage, the transmitter and the receiver repeat steps S1 and S2 several times to prepare quantum states that meet the set number, thereby each preparing n pairs of entangled states;

[0100] The transmitter and receiver prepare m coin position super-encoded single photons, each of which is randomly in a state of {|0>,|1>,|+>,|->}, where

[0101] The ordered sequence of the first particle formed by the entanglement pair created by quantum walking at the sending end (receiving end) is S A (S B ); the sender (receiver) inserts the single photon into the ordered sequence C consisting of the remaining partner photons of the entangled pair A (C B ) at a random position; at this time, the sequence S A There are n photons, sequence S B There are n photons, sequence C A There are n+m photons, sequence C B There are n+m photons. When the state of the coin is |0> and |1>, the circle is represented by -. When the state of the coin is |+> and |->, the circle is represented by +;

[0102] In particular, the entanglement preparation process here is different from the existing method of preparing first and then distributing. Instead, it distributes first and then automatically generates the required shared entangled state after one quantum walk;

[0103] Detection channel stage:

[0104] S3. Re-describe and measure the shared quantum channel; specifically, the steps include:

[0105] The quantum channel |φ>1 at the transmitter is redescribed as a position-based measurement basis {|-1>|0>,|1>,|2>} and a coin-based measurement basis {|+>,|->}, expressed as

[0106]

[0107] Set a sufficiently large subset selected from the entangled state set {|φ>1}; the sender first uses the measurement basis {|-1>|0>,|1>,|2>} to measure particle A1, and after obtaining the measured entangled state, it uses the measurement basis {|+>,|->} to measure another particle corresponding to the entangled state;

[0108] The quantum channel |φ>1 at the receiving end is redescribed as a position-based measurement basis {|-1>|0>,|1>,|2>} and a coin-based measurement basis {|+>,|->}, expressed as

[0109]

[0110] Set a subset selected from the entangled state set {|φ>1}; the receiving end first uses the measurement basis {|-1>|0>,|1>,|2>} to measure particle B1, and after obtaining the measured entangled state, uses the measurement basis {|+>,|->} to measure another particle corresponding to the entangled state.

[0111] S4. Detect the quantum channel to determine the security of the quantum channel; specifically, the steps include:

[0112] The transmitter detects the quantum channel by comparing the measurement result with four possible output results; the measurement output and the corresponding quantum state of the transmitter are

[0113] If the measurement result on A1 is 1 and the measurement result on A3 is 1, then the associated quantum state is |1>|+>;

[0114] If the measurement result on A1 is 1 and the measurement result on A3 is -1, then the associated quantum state is |1>|->;

[0115] The measurement result on A1 is -1 and the measurement result on A3 is 1, then the associated quantum state is |-1>|+>;

[0116] The measurement result on A1 is -1 and the measurement result on A3 is -1, then the associated quantum state is |-1>|->;

[0117] If the comparison error rate of all output results is lower than a set value (preferably a preset threshold of 2% to 8.9%), the sender determines that the quantum channel is secure and proceeds to the subsequent steps;

[0118] Otherwise, the sender determines that there may be a risk of eavesdropping, and the sender and receiver will terminate the current secret information communication and restart the protocol if necessary;

[0119] Similarly, the receiving end detects the quantum channel by comparing the measurement result with the four possible output results; the measurement output of the receiving end and the corresponding quantum state are

[0120] If the measurement result on B1 is 1 and the measurement result on B3 is 1, then the associated quantum state is |1>|+>;

[0121] If the measurement result on B1 is 1 and the measurement result on B3 is -1, then the associated quantum state is |1>|->;

[0122] The measurement result on B1 is -1 and the measurement result on B3 is 1, then the associated quantum state is |-1>|+>;

[0123] The measurement result on B1 is -1 and the measurement result on B3 is -1, then the associated quantum state is |-1>|->;

[0124] If the comparison error rate of all output results is lower than the set threshold, the sender determines that the quantum channel is secure and proceeds to the subsequent steps;

[0125] Otherwise, the receiving end determines that there may be a risk of eavesdropping, and the sending and receiving ends will terminate the current secret information communication and restart the protocol if necessary;

[0126] Third-party measurement phase: This phase aims to generate entangled states between the transmitter and the receiver through third-party measurement;

[0127] S5. The transmitter and the receiver are measured and entangled by a third party; specifically, the steps include:

[0128] The sender sends sequence C A Send to a third party; the receiving end sends sequence C B Sent to a third party; at the same time, ensure S A At the sending end, S B On the receiving end;

[0129] The third party receives C A and C B conduct The |φ'> basis measurement is used to measure the S A and S B The corresponding partner photons will become entangled, and this process is similar to entanglement exchange;

[0130] S6. According to the result of step S5, the transmitting end and the receiving end confirm the security of the shared quantum channel again; specifically, the steps include:

[0131] The transmitter sends m photons at C A The position of the photons is published, and the receiving end sends m photons to C BThe position in the announcement;

[0132] The sender exchanges the information of m photons with the receiver. Only when both parties are single photons during security inspection will the corresponding measurement result be used;

[0133] Determination of different photon combinations and corresponding effects, including

[0134] If C A is an entangled photon and C B For entangled photons, the corresponding effect is the entanglement exchange of message transmission;

[0135] If C A is a single photon and C B If it is a single photon, the corresponding function is safety check;

[0136] If C A is an entangled photon and C B If it is a single photon, there is no corresponding effect;

[0137] If C A is a single photon and C B For entangled photons, there is no corresponding effect;

[0138] By measuring single photons of the same basis, the sender and receiver estimate the error rate, thereby reconfirming the security of the quantum channel; interception by the attacker will trigger the single photon detection results of either party, which will be inconsistent with the basic information of the original single photon and lead to discovery;

[0139] Secret message transmission phase:

[0140] This stage aims to use the quantum channel constructed in the early stage to transmit secret information again through the characteristics of quantum walk. The sender and receiver discard S A and S B The photons that are not entangled in the exchange, then S A The entangled photons exchanged in the A , the entangled photons in SB form another ordered sequence M B In order to transmit the unknown quantum bit state, the present invention chooses to use another quantum walk. The sender has another particle A2, which carries another coin 2 state. At this time, the quantum walk model has a position space and two coin spaces. Suppose the sender wants to transmit the quantum state Encoded onto the A2 particle, this process can be achieved by executing the Hadamard gate H on the reference state |0> or |1>. In this type of task, quantum teleportation in quantum communication provides a superior solution, making full use of quantum entanglement as the basis of the quantum channel. In particular, quantum teleportation based on linear quantum walks improves the measurement efficiency after a quantum walk, and is easier to implement in experiments without the need to prepare the necessary entangled states in advance, but automatically generates them. To this end, the sender completes the communication task of the quantum state sequence in an orderly manner by executing quantum teleportation based on quantum walks, thereby realizing the communication of classical secret information.

[0141] S7. Merge the particles at the transmitting end and the receiving end to obtain a composite quantum state; specifically, the steps include:

[0142] The sending end introduces a new coin space particle A2, which merges the sending end particles A1 and A2 and the receiving end particle B1, where A1 and B1 are entangled together through the advantage of MDI, and the composite quantum state is obtained as follows:

[0143]

[0144] Where |ψ>0 is the composite quantum state of the communication system of particles A1 and A2 at the sending end and particle B1 at the receiving end; Refers to a specific quantum state formed by quantum entanglement between the sending particle A1 and the receiving particle B1 in this composite quantum system;

[0145] S8. Perform a second quantum walk on the obtained composite quantum state to obtain the quantum entangled state of the transmitter and the receiver; specifically, the steps include:

[0146] Perform the second quantum walk on the quantum state |ψ>0 Where W2 represents the final quantum state after the second quantum walk on the system composite quantum state |ψ>0, E2 represents the evolution operator of the second quantum walk, which describes the evolution process of the quantum state in this walk, and I P represents the unit operator acting on the position space, C2 represents the coin operator acting on the second coin space, here is the I (Identity) gate, and I2 represents the unit operator acting on the second position space;

[0147] Assume that the state of coin 2 on particle A2 is the control state, and the position state on particle A1 is the target state. Then the quantum entangled state obtained by the transmitter and the receiver is

[0148]

[0149] Where |ψ>1 is the entangled state of the quantum system after the second quantum walk.

[0150] S9. The sending end performs projection measurement on the quantum entangled state and sends the measurement result to the receiving end, thereby completing the final measurement device-independent quantum secure direct communication; specifically, the steps include:

[0151] The sender performs projection measurement of particles A2 and A1 on |ψ>1: the sender uses the measurement basis {|+>,|->} to measure A2, and the corresponding measurement output result is recorded as {1,-1}; the sender then uses the measurement basis Measure particle A1, where And record the corresponding measurement output result as {1,0,-1}; finally, the transmitter sends the measurement result to the receiver;

[0152] In order to transmit quantum states, the measurement results of the transmitter on particles A2 and A1 and the local forward operation of the receiver on particle B1 are related as follows:

[0153] The measurement result of the transmitter on particle A2 is {1,1} and the measurement result on particle A1 is {-1,1}, then the local unitary operation of the receiver on row B1 is I;

[0154] The measurement result of the transmitter on particle A2 is {1,-1} and the measurement result on particle A1 is {-1,-1}, then the local unitary operation of the receiver on row B1 is Z;

[0155] The measurement result of the transmitter on particle A2 is {1} and the measurement result on particle A1 is {0}, then the local unitary operation of the receiver on row B1 is X;

[0156] The measurement result of the transmitter on particle A2 is {-1} and the measurement result on particle A1 is {0}, so the local unitary operation of the receiver on row B1 is ZX;

[0157] Ultimately, quantum secure direct communication that is independent of the measurement device is achieved.

[0158] The present invention introduces a new QSDC protocol based on quantum walk, and uses its advantage of being independent of measurement equipment to develop the MDI-QW-QSDC protocol. The protocol uses a single-step quantum walk to prepare entangled states and a two-step quantum walk to establish a secure quantum channel, providing a basis for expanding possibilities in the field of QSDC. Further analysis shows that, in theory, the MDI-QW-QSDC protocol is unconditionally secure. Simply put, it proposes an innovative way to achieve secure communication using quantum walk technology. The MDI-QW-QSDC protocol not only improves the methods of preparing entangled states and establishing quantum channels, but also lays a theoretical foundation for realizing high-security quantum communications in the field of multi-party quantum secure communications in the future, and has broad application prospects.

Claims

1. A measurement device-independent quantum secure direct communication method based on quantum walk, comprising the following steps: S1. encoding a position state in a position space, and encoding a coin state in a coin space; S2. Perform a quantum walk based on a straight line to obtain a shared entangled state used as a quantum channel, completing the preparation of the quantum channel; S3. Re-describe and measure the shared quantum channel; S4. Detect the quantum channel to determine the security of the quantum channel; S5. The transmitter and receiver are measured and entangled by a third party; S6. According to the result of step S5, the sending end and the receiving end confirm the security of the quantum channel again; S7. Merge the particles at the transmitting end and the receiving end to obtain a composite quantum state; S8. Perform a second quantum walk on the obtained composite quantum state to obtain the quantum entangled state of the transmitter and the receiver; S9. The sending end performs projection measurement on the quantum entangled state and sends the measurement result to the receiving end, completing the final quantum secure direct communication that is independent of the measurement device.

2. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 1 is characterized in that The encoding of the position state in the position space and the encoding of the coin state in the coin space described in step S1 specifically include the following steps: Consider a measurement device-independent model based on quantum walk on a straight line. The model includes a position space and a coin space named coin 1. The sender holds particles A1 and A3. Encode the position state in the position space onto particle A1, and encode the coin 1 state in the coin 1 space onto particle A3; The initial states prepared by the sender on A1 and A3 are both |0>; The initial state of the quantum walk is expressed as in is the tensor product.

3. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 2 is characterized in that The execution described in step S2 is based on the quantum walk on a straight line, thereby obtaining a shared entangled state used as a quantum channel and completing the preparation of the quantum channel, which specifically includes the following steps: By performing a straight-line quantum walk on the quantum state |φ>0, the transmitter obtains a shared entangled state for the quantum channel. A quantum walk on a straight line is represented by Where W1 is the quantum walk operator on the first straight line; E1 is the conditional shift operator; I1 is the unit operator acting on the position space; C1 is the coin operator acting on the coin space 1 at the sending end; is the tensor product; S is the shift operator; is the conjugate transpose operator of S; After one step of quantum walk evolution on a straight line, the new quantum state is obtained: The transmitting end and the receiving end each repeat steps S1 and S2 several times to prepare quantum states that meet the set number, thereby each preparing n pairs of entangled states; The transmitter and receiver prepare m coin position super-encoded single photons, each of which is randomly in a state of {|0>,|1>,|+>,|->}, where The ordered sequence of the first particle formed by the entanglement pair created by the quantum walk at the sending end is S A ; The sender inserts the single photon into the ordered sequence C consisting of the remaining partner photons of the entangled pair A The random position of the receiving end; the ordered sequence of the first particle composed of the entangled pair created by quantum walking is S B ; The receiving end inserts the single photon into the ordered sequence C consisting of the remaining partner photons of the entangled pair B At this time, the sequence S A There are n photons, sequence S B There are n photons, sequence C A There are n+m photons, sequence C B There are n+m photons.

4. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 3 is characterized in that The re-describing and measuring the shared quantum channel in step S3 specifically includes the following steps: The quantum channel |φ>1 at the transmitter is redescribed as a position-based measurement basis {|-1>|0>,|1>,|2>} and a coin-based measurement basis {|+>,|->}, expressed as Set a subset selected from the entangled state set {|φ>1}; the sender first uses the measurement basis {|-1>|0>,|1>,|2>} to measure particle A1, and after obtaining the measured entangled state, it uses the measurement basis {|+>,|->} to measure another particle corresponding to the entangled state; The quantum channel |φ>1 at the receiving end is redescribed as a position-based measurement basis {|-1>|0>,|1>,|2>} and a coin-based measurement basis {|+>,|->}, expressed as Set a subset selected from the entangled state set {|φ>1}; the receiving end first uses the measurement basis {|-1>|0>,|1>,|2>} to measure particle B1, and after obtaining the measured entangled state, uses the measurement basis {|+>,|->} to measure another particle corresponding to the entangled state.

5. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 4 is characterized in that The step S4 of detecting the quantum channel to determine the security of the quantum channel specifically includes the following steps: The transmitter detects the quantum channel by comparing the measurement result with the four possible output results. The measurement output and the corresponding quantum state of the transmitter are: if the measurement result on A1 is 1 and the measurement result on A3 is 1, the associated quantum state is |1>|+>. If the measurement result on A1 is 1 and the measurement result on A3 is -1, then the associated quantum state is |1>|->; The measurement result on A1 is -1 and the measurement result on A3 is 1, then the associated quantum state is |-1>|+>; The measurement result on A1 is -1 and the measurement result on A3 is -1, then the associated quantum state is |-1>|->; If the comparison error rate of all output results is lower than the set threshold, the sender determines that the quantum channel is secure and proceeds to the subsequent steps; Otherwise, the sender determines that there may be a risk of eavesdropping; The receiving end detects the quantum channel by comparing the measurement result with the four possible output results; the measurement output of the receiving end and the corresponding quantum state are: the measurement result on B1 is 1 and the measurement result on B3 is 1, then the associated quantum state is |1>|+>; If the measurement result on B1 is 1 and the measurement result on B3 is -1, then the associated quantum state is |1>|->; The measurement result on B1 is -1 and the measurement result on B3 is 1, then the associated quantum state is |-1>|+>; The measurement result on B1 is -1 and the measurement result on B3 is -1, then the associated quantum state is |-1>|->; If the comparison error rate of all output results is lower than the set threshold, the sender determines that the quantum channel is secure and proceeds to the subsequent steps; Otherwise, the receiving end determines that there may be a risk of eavesdropping.

6. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 5 is characterized in that The transmitter and receiver described in step S5 are measured and entangled by a third party, which specifically includes the following steps: The sender sends sequence C A Send to a third party; the receiving end sends sequence C B Sent to a third party; at the same time, ensure S A At the sending end, S B On the receiving end; The third party receives C A and C B Conduct |φ'> basis measurements and publish the measurement results; By |φ'> basis measurement, S A and S B The corresponding partner photons will become entangled.

7. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 6 is characterized in that According to the result of step S5, the transmitting end and the receiving end confirm the security of the quantum channel again, which specifically includes the following steps: The transmitter sends m photons at C A The position of the photons is published, and the receiving end sends m photons to C B The position in the announcement; The sender exchanges the information of m photons with the receiver; Determination of different photon combinations and corresponding effects, including If C A is an entangled photon and C B For entangled photons, the corresponding effect is the entanglement exchange of message transmission; If C A is a single photon and C B If it is a single photon, the corresponding function is safety check; If C A is an entangled photon and C B If it is a single photon, there is no corresponding effect; If C A is a single photon and C B For entangled photons, there is no corresponding effect; By measuring single photons of the same basis, the sender and receiver estimate the error rate, thereby reconfirming the security of the quantum channel.

8. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 7 is characterized in that The step S7 of merging the particles at the transmitting end and the receiving end to obtain a composite quantum state specifically includes the following steps: The sending end introduces a new coin space particle A2, which merges the sending end particles A1 and A2 and the receiving end particle B1, where A1 and B1 are entangled together through the advantage of MDI, and the composite quantum state is obtained as follows: Where |ψ>0 is the composite quantum state of the communication system of particles A1 and A2 at the sending end and particle B1 at the receiving end; It refers to a quantum state formed by quantum entanglement between particle A1 at the sending end and particle B1 at the receiving end in this composite quantum system.

9. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 8 is characterized in that The second step of quantum walking is performed on the obtained composite quantum state in step S8 to obtain the quantum entangled state of the transmitting end and the receiving end, which specifically includes the following steps: Perform the second quantum walk on the quantum state |ψ>0 Among them W 2 represents the final quantum state after the second quantum walk on the system composite quantum state |ψ>0, E2 represents the evolution operator of the second quantum walk, I P represents the unit operator acting on the position space, C2 represents the coin operator acting on the second coin space, and I2 represents the unit operator acting on the second position space; Assume that the state of coin 2 on particle A2 is the control state, and the position state on particle A1 is the target state. Then the quantum entangled state obtained by the transmitter and the receiver is Where |ψ>1 is the entangled state of the quantum system after the second quantum walk.

10. The measurement device-independent quantum secure direct communication method based on quantum walk according to claim 9, characterized in that The transmitting end in step S9 performs projection measurement on the quantum entangled state and sends the measurement result to the receiving end, thereby completing the final measurement device-independent quantum secure direct communication, which specifically includes the following steps: The sender performs projection measurement of particles A2 and A1 on |ψ>1: the sender uses the measurement basis {|+>,|->} to measure A2, and the corresponding measurement output result is recorded as {1,-1}; the sender then uses the measurement basis Measure particle A1, where And record the corresponding measurement output result as {1,0,-1}; finally, the transmitter sends the measurement result to the receiver; In order to transmit quantum states, the measurement results of the transmitter on particles A2 and A1 and the local forward operation of the receiver on particle B1 are related as follows: The measurement result of the transmitter on particle A2 is {1,1} and the measurement result on particle A1 is {-1,1}, then the local unitary operation of the receiver on row B1 is I; The measurement result of the transmitter on particle A2 is {1,-1} and the measurement result on particle A1 is {-1,-1}, then the local unitary operation of the receiver on row B1 is Z; The measurement result of the transmitter on particle A2 is {1} and the measurement result on particle A1 is {0}, then the local unitary operation of the receiver on row B1 is X; The measurement result of the transmitter on particle A2 is {-1} and the measurement result on particle A1 is {0}, so the local unitary operation of the receiver on row B1 is ZX; Ultimately, quantum secure direct communication that is independent of the measurement device is achieved.

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