Quantum walk based measurement-device-independent quantum secure direct communication method

Abstract

The application discloses a kind of measurement equipment independent quantum secure direct communication methods based on quantum walk, including encoding in position space in position state and in hardware space in coin state;It is obtained based on quantum walk on straight line that shared entangled state is used as quantum channel;The shared quantum channel is re-described and measured;Quantum channel is detected and the security of quantum channel is judged;Sender and receiver measure and entangle through third party;Sender and receiver confirm the security of quantum channel again;The particle of sender and receiver is merged to obtain composite quantum state;Second quantum walk is carried out to obtain the quantum entangled state of sender and receiver;Sender carries out projection measurement on quantum entangled state and sends the measurement result to receiver, and completes the final measurement equipment independent quantum secure direct communication.The application can realize measurement equipment independent quantum secure direct communication, and reliability is high, and security is good.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of quantum communication, and particularly relates to a measurement-device-independent quantum secure direct communication method based on quantum walk. BACKGROUND

[0002] With the development of economy and technology and the improvement of people's living standards, people's demand for information security is also 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. inherent uncertainty of quantum mechanics, measurement collapse and non-cloning). Therefore, it has also received more and more attention.

[0003] As a core technology of quantum communication, quantum key distribution (QKD) has been widely studied in both theory and experiment. Quantum key distribution allows parties to share secure random keys for message transmission without being limited by physical distance. At the same time, as another important part of quantum communication, quantum secure direct communication (QSDC) allows communication parties to directly transmit secret messages over a quantum channel without providing a pre-shared key. In this sense, QSDC not only saves quantum resources, but also avoids potential security risks related to keys and ciphertexts, thereby reducing the complexity of the communication system.

[0004] QSDC protocols have perfect quantum sources, noiseless channels, perfect devices and detectors, and are completely secure in an ideal environment. However, in the real world, quantum communication systems often have imperfect devices, especially measurement devices; these imperfections can cause potential security threats, such as eavesdroppers who may exploit these device vulnerabilities to steal information. Therefore, the current QSDC scheme indeed has the problems of low security and poor reliability. SUMMARY

[0005] The purpose of the present application 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 application comprises the following steps:

[0007] S1. Encoding position states located in position space and coin states located in coin space;

[0008] S2. Performing quantum walk based on a straight line to obtain shared entangled states used as quantum channels, thereby completing the preparation of quantum channels;

[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 sender and the receiver measure and entangle through a third party;

[0012] S6. According to the result of step S5, the sender and the receiver reconfirm the security of the quantum channel;

[0013] S7. Merge the particles of the sender and the receiver to obtain a composite quantum state;

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

[0015] S9. The sender performs a projection measurement on the quantum entangled state and sends the measurement result to the receiver, completing the final measurement-device-independent quantum secure direct communication.

[0016] The encoding of step S1 is a position state located in a position space, and a coin state located in a coin space, specifically including 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 located in the position space onto particle A1, and encode the coin 1 state located in the coin 1 space onto particle A3;

[0019] Assume that the sender prepares the initial state on A1 and A3 as |0>;

[0020] The initial state of the quantum walk is represented as where is a tensor product.

[0021] Step S2 described performing quantum walk on a straight line to obtain a shared entangled state used as a quantum channel, completing the preparation of the quantum channel, specifically including the following steps:

[0022] Perform quantum walk on a straight line on the quantum state |φ>0, and the sender obtains a shared entangled state for the quantum channel;

[0023] The quantum walk on a straight line is represented as

[0024]

[0025] where W1 is the one-step straight-line quantum walk operator; E1 is the conditional shift operator; I1 is the identity operator acting on the position space; C1 is the coin operator acting on the sender's coin space 1, which can be an arbitrary single-qubit operation such as the identity gate or Hadamard gate, and is assumed to be the Hadamard gate (H) in this case; is the tensor product; S is the shift operator; denotes the conjugate transpose (Hermitian conjugate) of S, which is often used for the inverse operation;

[0026] After one-step straight-line quantum walk evolution, the new quantum state is

[0027]

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

[0029] The sender and the receiver prepare m single photons of the coin-position-like supercode, each of which is randomly in one of the states {|0>, |1>, |+>, |->}, where

[0030] The ordered sequence of the first particle group composed of the entangled pair prepared by the sender (receiver) through quantum walk is S A (S B ); the sender (receiver) inserts the single photon into a random position of the ordered sequence C A (C B ) composed of the partner photons remaining from the entangled pair; at this time, sequence S A has n photons, sequence S B has n photons, sequence C A has n+m photons, and sequence C B has n+m photons.

[0031] The step S3 described above for re-describing and measuring the quantum channel includes the following steps:

[0032] The sender's quantum channel |φ>1 is re-described as a position-based measurement basis {|-1>|0>, |1>, |2>} and a coin-based measurement basis {|+>, |->}, and is represented as

[0033]

[0034] A subset is set from the entangled state set { | φ > 1} ; the sending end first measures particle A1 by using the measurement basis { | -1 > | 0 >, | 1 >, | 2 >}, obtains the measured entangled state, and then measures another particle corresponding to the entangled state by using the measurement basis { | + >, | - >}.

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

[0036]

[0037] A subset is set from the entangled state set { | φ > 1} ; the receiving end first measures particle B1 by using the measurement basis { | -1 > | 0 >, | 1 >, | 2 >}, obtains the measured entangled state, and then measures another particle corresponding to the entangled state by using the measurement basis { | + >, | - >}.

[0038] The quantum channel is detected in step S4, so as to judge the security of the quantum channel, and specifically includes the following steps:

[0039] The sending end detects the quantum channel by comparing the measurement result with four possible output results; the measurement output of the sending end and the corresponding quantum state are as follows:

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

[0043] If 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 error rate of all output results is lower than a set threshold, then the sending end judges that the quantum channel is safe, and continues the subsequent steps;

[0045] Otherwise, the sending end judges that there is a risk of eavesdropping.

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

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

[0050] If 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 a set threshold, the receiving end judges that the quantum channel is safe, and continues with the subsequent steps;

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

[0053] The sending end and the receiving end in step S5 perform measurement and entanglement through a third party, and the specific steps include the following steps:

[0054] The sending end sends the sequence C A to the third party; the receiving end sends the sequence C B to the third party; and S A is ensured. B At the sending end, S A At the receiving end.

[0055] The third party performs basis measurement on the received C B and C A , and publishes the measurement results; through |φ'> basis measurement, the corresponding partner photons in S B and S A will be entangled, and this process is similar to entanglement exchange.

[0056] According to the results of step S5, the sending end and the receiving end in step S6 reconfirm the security of the shared quantum channel, and the specific steps include the following steps:

[0057] The sending end publishes the positions of the m photons in C B , and the receiving end publishes the positions of the m photons in C A .

[0058] The sending end exchanges the information of the m photons with the receiving end.

[0059] The determination of different photon combinations and corresponding effects includes

[0060] If C B ​For entangled photons, the corresponding action is the entangled exchange of messages;

[0061] If C A is a single photon and C B is a single photon, the corresponding action is security check;

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

[0063] If C A is a single photon and C B is an entangled photon, there is no corresponding action;

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

[0065] The step S7 of merging the particles of the sender and the receiver to obtain a composite quantum state includes the following steps:

[0066] The sender introduces a new coin space particle A2, and merges the particles A1 and A2 of the sender and the particle B1 of the receiver, wherein A1 and B1 are entangled through the advantage of MDI, and the composite quantum state is

[0067]

[0068] In the formula, |ψ>0 is the composite quantum state of the communication system of the particles A1 and A2 of the sender and the particle B1 of the receiver; It refers to a specific quantum state formed by the quantum entanglement of the particle A1 of the sender and the particle B1 of the receiver in this composite quantum system.

[0069] The step S8 of performing a second quantum walk on the obtained composite quantum state to obtain a quantum entangled state of the sender and the receiver includes the following steps:

[0070] Performing a second quantum walk on the quantum state |ψ>0 Wherein 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 step walk, I P represents the unit operator acting on the position space, C2 represents the coin operator acting on the second coin space, which is an I (Identity) gate here, and I2 represents the unit operator acting on the second position space;

[0071] The coin 2 state located on the particle A2 is set as a control state, and the position state located on the particle A1 is set as a target state, so that the quantum entangled state obtained by the sending end and the receiving end is

[0072]

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

[0074] The sending end in step S9 performs projection measurement on the quantum entangled state, and sends the measurement result to the receiving end, so as to complete the final measurement-device-independent quantum secure direct communication, and the specific steps include the following steps.

[0075] The sending end performs projection measurement on the particles A2 and A1 on |ψ>1: the sending end measures A2 by using the measurement basis {|+>, |->}, and the corresponding measurement output result is recorded as {1, -1}; the sending end measures A1 by using the measurement basis The particle A1 is measured, wherein And the corresponding measurement output result is recorded as {1, 0, -1}; finally, the sending end sends the measurement result to the receiving end.

[0076] In order to transmit the quantum state, the measurement result of the sending end on the particles A2 and A1 and the local positive operation of the receiving end on the particle B1 are in a relationship as follows:

[0077] When the measurement result of the sending end on the particle A2 is {1, 1} and the measurement result on the particle A1 is {-1, 1}, the local unitary operation of the receiving end on B1 is I;

[0078] When the measurement result of the sending end on the particle A2 is {1, -1} and the measurement result on the particle A1 is {-1, -1}, the local unitary operation of the receiving end on B1 is Z;

[0079] When the measurement result of the sending end on the particle A2 is {1} and the measurement result on the particle A1 is {0}, the local unitary operation of the receiving end on B1 is X;

[0080] When the measurement result of the sending end on the particle A2 is {-1} and the measurement result on the particle A1 is {0}, the local unitary operation of the receiving end on B1 is ZX;

[0081] Finally, the measurement-device-independent quantum secure direct communication is completed.

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

[0083] Figure 1 A schematic diagram of the method flow of the method of the present application. DETAILED DESCRIPTION

[0084] As Figure 1 A schematic diagram of the method flow of the method of the present application is shown: the measurement-device-independent quantum secure direct communication method based on quantum walk provided by the present application includes the following steps:

[0085] Quantum channel preparation stage: this stage aims to prepare an entangled state as a quantum channel to meet the communication needs of the sender Alice and the receiver Bob;

[0086] S1. Encoding the position state in the position space and the coin state in the coin space; specifically including 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, and the sender holds particles A1 and A3;

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

[0089] The sender prepares the initial state on A1 and A3 as |0>;

[0090] The initial state of the quantum walk is represented as Where is a tensor product;

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

[0092] Perform quantum walk on a straight line on the quantum state |φ>0, and the sender obtains a shared entangled state for the quantum channel;

[0093] The quantum walk on a straight line is represented as

[0094]

[0095] In the formula, W1 is the first-step quantum walk operator on a straight line; E1 is a conditional shift operator; I1 is a unit operator acting on the position space; C1 is a coin operator acting on the sender's coin space 1, which can be any single-qubit operation such as a unit gate, Hadamard gate, etc., and is assumed to be a H (Hadamard) gate here; is a tensor product; S is a shift operator; The conjugate transpose (Hermitian conjugate) of S, commonly used for inversion;

[0096] After one step of quantum walk evolution, the new quantum state is

[0097]

[0098] The sender and 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;

[0099] In order to prepare for the subsequent detection channel and entangled state preparation stage, the sender and 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 sender and receiver prepare m coin position super-encoded single photons, each randomly in one of the states {|0>, |1>, |+>, |->}, where

[0101] The sender (receiver) forms an ordered sequence S A (S B ) from the first particle pair prepared by quantum walk entanglement; the sender (receiver) inserts a single photon into a random position of the ordered sequence C A (C B ) composed of the remaining partner photons of the entangled pair; at this time, sequence S A has n photons, sequence S B has n photons, sequence C A has n+m photons, and sequence C B has 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, but rather distributing first and then automatically generating the required shared entangled state after one step of quantum walk;

[0103] Detection channel stage:

[0104] S3. Redescribe and measure the shared quantum channel; specifically including the following steps:

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

[0106]

[0107] A set of entangled states is selected from the set of entangled states |φ>1; the sender first measures particle Al using the measurement basis | -1 >|0>, |1>, |2>}, and then measures another particle corresponding to the measured entangled state using the measurement basis | + >, | - >};

[0108] The quantum channel |φ>1 of the receiver is re-described as a position-based measurement basis | -1 >|0>, |1>, |2>}, and a coin-based measurement basis | + >, | - >}, and is represented as

[0109]

[0110] A set of entangled states is selected from the set of entangled states |φ>1; the receiver first measures particle Bl using the measurement basis | -1 >|0>, |1>, |2>}, and then measures another particle corresponding to the measured entangled state using the measurement basis | + >, | - >}.

[0111] S4. The quantum channel is detected to determine the security of the quantum channel; specifically including the following steps:

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

[0113] The measurement result on Al is 1 and the measurement result on A3 is 1, and the associated quantum state is |1>|+>;

[0114] The measurement result on Al is 1 and the measurement result on A3 is -1, and the associated quantum state is |1>| - >;

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

[0116] The measurement result on Al is -1 and the measurement result on A3 is -1, and 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 safe, and continues with the subsequent steps;

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

[0119] Similarly, the receiver performs quantum channel detection by comparing the measurement result with four possible outputs; the receiver's measurement output 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] If the measurement result on B1 is -1 and the measurement result on B3 is 1, then the associated quantum state is |-1>|+>.

[0123] If 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 error rate of all output results is lower than the set threshold, the sending end determines that the quantum channel is secure and continues with subsequent steps.

[0125] Otherwise, if the receiving end determines that there may be a risk of eavesdropping, the sending and receiving ends will suspend 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 sender and receiver through third-party measurement;

[0127] S5. The sending and receiving ends perform measurement and entanglement through a third party; specifically, this includes the following steps:

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

[0129] The third party receives C A and C B conduct Baseline measurement, and publication of measurement results. Through |φ'> baseline measurement, S A and S B The corresponding partner photons will become entangled, a process similar to entanglement swapping.

[0130] S6. Based on the result of step S5, the transmitting end and the receiving end reconfirm the security of the shared quantum channel; specifically, this includes the following steps:

[0131] The transmitter sends m photons at C A The location in the middle is announced, and the receiving end will send m photons in C. Bposition announcement in S

[0132] The sending end exchanges the information of m photons with the receiving end, and only in the case of single photons for both ends during security check, the corresponding measurement result is used;

[0133] The determination of different photon combinations and corresponding effects includes

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

[0135] If C A is a single photon and C B is a single photon, the corresponding effect is security check;

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

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

[0138] Through the measurement of single photons of the same base, the sending end and the receiving end estimate the error rate, thereby confirming the security of the quantum channel again; the interception of the attack end will trigger the single photon detection result of any one party, thereby being inconsistent with the original single photon basis information and being discovered;

[0139] Secret message transmission stage:

[0140] This stage aims to use the quantum channel constructed in the previous stage to transmit secret information again through the characteristics of quantum walk. The sending end and the receiving end discard the photons in S A and S B that are not entangled exchanged, and then the entangled exchanged photons in S A form an ordered sequence M A , and the entangled exchanged photons in SB form another ordered sequence M B . In order to transmit unknown quantum bit states, the present application selects to use another quantum walk. The sending end has another particle A2, which carries another coin 2 state. At this time, the quantum walk model has position space and two coin space. Assuming that the sending end wants to transmit quantum state Encoding to A2 particle, this process can be achieved by performing Hadamard gate H on the reference state |0> or |1>. In this kind of task, quantum teleportation in quantum communication provides an excellent solution, using quantum entanglement as the basis of quantum channel. Especially the quantum teleportation based on straight quantum walk, after one step quantum walk, the measurement efficiency is improved, and it is easier to realize in experiment, without the need to prepare the necessary entangled state in advance, but automatically generated. For this, the sender completes the communication task of quantum state sequence by performing quantum teleportation based on quantum walk, so as to realize the communication of classical secret information.

[0141] S7. The particles of the sender and the receiver are combined to obtain a composite quantum state; specifically comprising the following steps:

[0142] The sender introduces a new coin space particle A2, and combines the particles A1, A2 of the sender and the particles B1 of the receiver, wherein A1 and B1 are entangled by MDI, to obtain a composite quantum state

[0143]

[0144] In the formula, |ψ>0 is the composite quantum state of the particles A1, A2 of the sender and the particles B1 of the receiver in the communication system; It refers to a specific quantum state formed by quantum entanglement between the particles A1 of the sender and the particles B1 of the receiver in this composite quantum system;

[0145] S8. Perform the second step quantum walk on the obtained composite quantum state to obtain the quantum entangled state of the sender and the receiver; specifically comprising the following steps:

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

[0147] Set the coin 2 state located on the particle A2 as the control state, and the position state located on the particle A1 as the target state, then the quantum entangled state obtained by the sender and the receiver is

[0148]

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

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

[0151] The sending end performs projection measurement of particles A2 and A1 on |ψ>1: the sending end measures A2 by using the measurement basis Measure particle A1, wherein and record the corresponding measurement output result as {1, 0, -1}; finally, the sending end sends the measurement result to the receiving end;

[0152] In order to transmit the quantum state, the measurement result of the sending end on particles A2 and A1 and the local positive operation relationship of the receiving end on particle B1 are

[0153] If the measurement result of the sending end on particle A2 is {1, 1} and the measurement result on particle A1 is {-1, 1}, then the local unitary operation of the receiving end on B1 row is I;

[0154] If the measurement result of the sending end on particle A2 is {1, -1} and the measurement result on particle A1 is {-1, -1}, then the local unitary operation of the receiving end on B1 row is Z;

[0155] If the measurement result of the sending end on particle A2 is {1} and the measurement result on particle A1 is {0}, then the local unitary operation of the receiving end on B1 row is X;

[0156] If the measurement result of the sending end on particle A2 is {-1} and the measurement result on particle A1 is {0}, then the local unitary operation of the receiving end on B1 row is ZX;

[0157] Finally, the measurement-device-independent quantum secure direct communication is completed.

[0158] The application introduces a new QSDC protocol based on quantum walk, and develops the MDI-QW-QSDC protocol by using the advantage of measurement-device-independence. The protocol uses single-step quantum walk to prepare entangled states, and uses two-step quantum walk to establish a secure quantum channel, which provides a basis for expanding the possibility in the field of QSDC. Further analysis shows that the MDI-QW-QSDC protocol is unconditionally secure in theory. In short, an innovative way is proposed to realize secure communication by using quantum walk technology. The MDI-QW-QSDC protocol not only perfects the method of entangled state preparation and quantum channel establishment, but also lays a theoretical foundation for realizing high-security quantum communication in the field of multi-party quantum secure communication in the future, and has wide application prospect.

Claims

1. A quantum walk based measurement-device-independent quantum secure direct communication method, comprising the following steps: S1. encoding a position state in a position space and encoding a coin state in a coin space; S2. performing quantum walk on a straight line to obtain shared entangled states used as quantum channels, and completing preparation of quantum channels; specifically comprising the following steps: performing quantum walk on a straight line on a quantum state |φ>0, and obtaining shared entangled states used as quantum channels by a sending end; quantum walk on a straight line is expressed as where W1 is the first step straight line quantum walk operator; E1 is a conditional shift operator; I1 is the identity operator acting on the position space; C1 is a coin operator acting on the sender's coin space 1; is a tensor product; S is a shift operator; is the conjugate transpose operator of S; after one step of quantum walk on a straight line evolution, a new quantum state is obtained the sending end and the receiving end each repeat steps S1 and S2 several times to prepare quantum states satisfying a set number, thereby each preparing n pairs of entangled states; The sending end and the receiving end prepare m single photons of super-encoding of coin position, each photon randomly in one of the states {|0>, |1>, |+>, |->} The ordered sequence of the first particle in the entangled pairs created by the transmitter through a quantum walk is S. A The transmitter inserts a single photon into an ordered sequence C consisting of the remaining partner photons of the entangled pair. A The random position; the ordered sequence of the first particle formed by the entangled pairs created by the receiver through quantum walk is S. B The receiver inserts a single photon into an ordered sequence C consisting of the remaining partner photons of the entangled pair. B The random position; at this time, sequence S A There are n photons, and the sequence is S. B There are n photons, and the sequence is C. A There are n+m photons, sequence C B There are n+m photons; S3. re-describing and measuring the shared quantum channels; specifically comprising the following steps: the quantum channel |φ>1 of the sending end is re-described as a position-based measurement basis {|-1>|0>, |1>, |2>} and a coin-based measurement basis {|+>, |->}, and is expressed as a subset is set from the entangled state set {|φ>1}; the sending end first measures particle A1 using the measurement basis {|-1>|0>, |1>, |2>}, and then measures another particle corresponding to the measured entangled state using the measurement basis {|+>, |->}; the quantum channel |φ>1 of the receiving end is re-described as a position-based measurement basis {|-1>|0>, |1>, |2>} and a coin-based measurement basis {|+>, |->}, and is expressed as a subset is set from the entangled state set {|φ>1}; the receiving end first measures particle B1 using the measurement basis {|-1>|0>, |1>, |2>}, and then measures another particle corresponding to the measured entangled state using the measurement basis {|+>, |->}; S4. detecting the quantum channels to judge the security of the quantum channels; S5. the sending end and the receiving end measuring and entangling through a third party; specifically comprising the following steps: The sender sends the sequence C A to the third party; the receiver sends the sequence C B to the third party; meanwhile, S A is guaranteed at the sender B at the receiver The third party performs a measurement on the received C A and C B performs a measurement on |φ'> and publishes the measurement result; By measuring the |φ'> basis, S A and S B The corresponding partner photons in S will be entangled; S6. according to the result of step S5, the sending end and the receiving end again confirm the security of the quantum channels; specifically comprising the following steps: The sending end publishes the positions of the m photons in C A , and the receiving end publishes the positions of the m photons in C B . the sending end exchanges information of m photons with the receiving end; determination of different photon combinations and corresponding actions, including If C A is an entangled photon and C B is an entangled photon, then the corresponding action is an entangled exchange of messages. If C A is a single photon and C B is a single photon, then the corresponding action is a security check; If C A is an entangled photon and C B is a single photon, then there is no corresponding action; If C A is a single photon and C B is an entangled photon, there is no corresponding action; through measurement of single photons of the same basis, the sending end and the receiving end estimate the error rate to again confirm the security of the quantum channels; S7. merging the particles of the sending end and the receiving end to obtain a composite quantum state; S8. performing a second quantum walk on the obtained composite quantum state to obtain quantum entangled states of the sending end and the receiving end; S9. the sending end performs projection measurement on the quantum entangled states and sends the measurement result to the receiving end, completing the final measurement-device-independent quantum secure direct communication.

2. The quantum walk based measurement-device-independent quantum secure direct communication method of claim 1, wherein The encoding of the position state in the position space and the encoding of the coin state in the coin space in step S1 specifically comprise the following steps: considering 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, and the sending end holds particles A1 and A3; Encode the position state in the position space to particle A1, and encode the coin 1 state in the coin 1 space to particle A3; The sending end prepares the initial state of A1 and A3 as |0>; The initial state of the quantum walk is represented as where is the tensor product.

3. The quantum walk based measurement-device-independent quantum secure direct communication method of claim 2, wherein The step S4 detects the quantum channel, thereby judging the security of the quantum channel, and specifically includes the following steps: The sending end detects the quantum channel by comparing the measurement results with the four possible output results; the measurement output of the sending end and the corresponding quantum state are as follows: the measurement result of A1 is 1 and the measurement result of A3 is 1, and the associated quantum state is |1> |+>; The measurement result of A1 is 1 and the measurement result of A3 is -1, and the associated quantum state is |1> |->; The measurement result of A1 is -1 and the measurement result of A3 is 1, and the associated quantum state is |-1> |+>; The measurement result of A1 is -1 and the measurement result of A3 is -1, and the associated quantum state is |-1> |->; If the comparison error rate of all output results is lower than the set threshold, the sending end judges that the quantum channel is safe, and continues the subsequent steps; Otherwise, the sending end judges that there may be eavesdropping risk; The receiving end detects the quantum channel by comparing the measurement results with the four possible output results; the measurement output of the receiving end and the corresponding quantum state are as follows: the measurement result of B1 is 1 and the measurement result of B3 is 1, and the associated quantum state is |1> |+>; The measurement result of B1 is 1 and the measurement result of B3 is -1, and the associated quantum state is |1> |->; The measurement result of B1 is -1 and the measurement result of B3 is 1, and the associated quantum state is |-1> |+>; The measurement result of B1 is -1 and the measurement result of B3 is -1, and the associated quantum state is |-1> |->; If the comparison error rate of all output results is lower than the set threshold, the sending end judges that the quantum channel is safe, and continues the subsequent steps; Otherwise, the receiving end judges that there may be eavesdropping risk.

4. The quantum walk based measurement-device-independent quantum secure direct communication method of claim 3, wherein The step S7 combines the particles of the sending end and the receiving end to obtain a composite quantum state, and specifically includes the following steps: The sending end introduces a new coin space particle A2, and combines the particles A1 and A2 of the sending end and the particle B1 of the receiving end, wherein A1 and B1 are entangled through the advantage of MDI, to obtain a composite quantum state In the formula, |ψ>0 is a composite quantum state of the particles A1, A2 of the sending end and the particle B1 of the receiving end of the communication system. It is referred to as a quantum state formed by quantum entanglement of the particle A1 of the sending end and the particle B1 of the receiving end in the composite quantum system.

5. The quantum walk based measurement-device-independent quantum secure direct communication method of claim 4, wherein The step S8 performs a second quantum walk on the obtained composite quantum state to obtain a quantum entanglement state of the sending end and the receiving end, and specifically includes the following steps: Performing a second quantum walk on a quantum state |ψ>0 wherein wherein W 2 represents the final quantum state after the second step quantum walk on the system composite quantum state |ψ>0, E2 represents the evolution operator of the second step quantum walk, I P represents the unit operator acting on the position space, C2 represents the coin operator acting on the second coin space, I2 represents the unit operator acting on the second position space; Set the coin 2 state located on the particle A2 as a control state, and the position state located on the particle A1 as a target state, so that the sending end and the receiving end obtain a quantum entanglement state Wherein |ψ>1 is the entanglement state of the quantum system after the second quantum walk.

6. The quantum walk based measurement-device-independent quantum secure direct communication method of claim 5, wherein The step S9 performs projection measurement on the quantum entanglement state by the sending end, and sends the measurement result to the receiving end, to complete the final measurement device-independent quantum secure direct communication, and specifically includes the following steps: The sending end performs projection measurement of particles A2 and A1 on |ψ>1: the sending end measures A2 by using the measurement basis Measuring particle A1, wherein and records the corresponding measurement output results as {1, 0, -1}; finally, the sending end sends the measurement results to the receiving end; In order to transmit the quantum state, the measurement result of the sending end on particles A2 and A1 and the local positive operation relationship of the receiving end on particle B1 are as follows The measurement result of the sending end on particle A2 is {1, 1} and the measurement result on particle A1 is {-1, 1}, and then the local unitary operation of the receiving end on the B1 row is I; The measurement result of the sending end on particle A2 is {1, -1} and the measurement result on particle A1 is {-1, -1}, and then the local unitary operation of the receiving end on the B1 row is Z; The measurement result of the sending end on particle A2 is {1} and the measurement result on particle A1 is {0}, and then the local unitary operation of the receiving end on the B1 row is X; The measurement result of the sending end on particle A2 is {-1} and the measurement result on particle A1 is {0}, and then the local unitary operation of the receiving end on the B1 row is ZX; Finally, the measurement device-independent quantum secure direct communication is completed.

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