CN108847939B - A Quantum Network-Based MDI-QKD Method - Google Patents

Abstract

The invention discloses a quantum network-based MDI-QKD protocol, which applies quantum teleportation in the quantum network to the traditional unilateral MDI-QKD protocol. On the one hand, the advantages of the original MDI-QKD protocol are maintained, That is to ensure that the security protocol is independent of the measuring equipment, and effectively avoid all attacks on the measuring device in the QKD system; on the other hand, the quantum teleportation in the quantum network can greatly extend the safe distance of communication; the present invention The application of quantum teleportation in the quantum network to the MDI‑QKD protocol greatly improves the distance of the MDI‑QKD protocol while ensuring communication security.

Description

A Quantum Network-Based MDI-QKD Method

technical field

The invention belongs to the technical field of quantum communication, in particular to a quantum network-based MDI-QKD protocol.

Background technique

Quantum secure communication is based on quantum physics and informatics, and its security is guaranteed by the basic principles of quantum mechanics. Quantum key distribution is the most important content in quantum secure communication and is considered to be the most secure encryption method. It enables communicating parties to generate and share a random, secure key to encrypt and decrypt messages. In 1984, Bennett et al. first proposed the QKD protocol in the history of quantum cryptography, the BB84 protocol. After more than 30 years of development, various new QKD protocols have appeared one after another, such as: cyclic differential phase shift protocol, QKD based on pulse modulation protocol, decoy two-way QKD protocol, etc. Among them, Hoi-KwongLo et al. proposed a more practical QKD protocol in 2012, the Measurement-Device-Independent Quantum Key Distribution Protocol (MDI-QKD) protocol. In the MDI-QKD protocol, Alice and Bob are legitimate communication users, and are only responsible for the preparation of quantum states, and then send the prepared quantum states to Charlie, a third-party running the protocol, and Charlie completes the measurement of the two quantum states. The measurement results are announced to Alice and Bob through the public classic channel, and Alice and Bob perform subsequent processing on the data in their respective hands according to the measurement results on Charlie's side, and finally obtain the security key. Since the MDI-QKD protocol was first proposed in 2012, it has been popular among scientific research enthusiasts, and in-depth research has been carried out from both theoretical and experimental aspects.

Quantum network is a new type of secure communication network, which uses quantum entanglement and quantum teleportation to bring real security to the network and a qualitative leap in the fields of computing and science. Among them, quantum teleportation, also known as quantum teleportation, quantum teleportation, etc., is a new communication technology that uses quantum entanglement and some classical physical information to transmit unknown quantum states. If Alice transmits an unknown quantum state to the receiver Bob, firstly, Alice and Bob must share an entangled quantum channel, that is, the EPR entangled particle pair, and then Alice decomposes the original unknown quantum state into classical information and quantum information through the classical channel and The quantum channel is transmitted to Bob, and Bob restores the unknown quantum state according to the obtained information. Among them, the classical information is the measurement result obtained from the Bell state measurement of the unknown quantum state to be transmitted by the sender Alice, and the quantum information is the remaining information about the unknown quantum state that Alice did not acquire in the measurement.

In the original MDI-QKD protocol, legitimate communication users Alice and Bob are not equipped with any measurement devices, and are only responsible for the preparation of quantum states, which are measured by an untrusted third party, Charlie. The patent with the application number of 201510008068.9 discloses a two-node measurement device-independent quantum key distribution system. Two independent lasers and measurement device Charlie are placed on the same node, that is, placed on the Alice side or the Bob side, forming two A quantum key distribution system with bidirectional transmission of nodes. This special structure removes the eavesdropper's attack on the measurement equipment during the operation of the protocol and ensures the security of communication. However, the secure communication distance of the protocol is not long enough, and further improvement is needed to extend the secure communication distance.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a quantum network-based MDI-QKD protocol for the problems existing in the prior art, and apply quantum teleportation to the MDI-QKD protocol. On the other hand, quantum teleportation in the quantum network can greatly extend the safe distance of communication; therefore, a quantum network-based MDI- The QKD protocol can achieve the effect of greatly extending the safe transmission distance while ensuring security.

For achieving the above object, the technical scheme adopted in the present invention is:

A quantum network-based MDI-QKD protocol, including the following steps:

S1, the communication user Alice establishes an optimal routing route with the node Alice in the same quantum network by means of quantum routing;

S2, communication users Alice and Bob in the same quantum network prepare quantum states respectively, and communication user Alice transmits the quantum state prepared by himself to the node Alice through teleportation;

S3, after receiving the quantum state, Alice and Bob synchronously send the two quantum states to the third-party quantum measurement device Charlie through the quantum channel for measurement;

S4, Charlie performs BELL state measurement (BSM) on the received two quantum states, and then announces the measurement results to communication users Alice and Bob through the classical channel; Alice and Bob judge the obtained measurement results;

S5, if it is judged that the measurement result is wrong, Alice and Bob both discard the quantum state data sent to Charlie for measurement during this communication process; if it is judged that the measurement result is correct, Alice and Bob temporarily retain the quantum state data, and pass the basic After the operation obtains the sieved key data, either Alice or Bob performs a bit flip on its own key;

S6, repeat steps S2 to S5, obtain a string of natural key bits;

S7, detect whether there is eavesdropping on the quantum channel;

S8, get the final security key.

Specifically, in step S2, the communication user Alice will lose a certain amount of information in the process of transmitting the quantum state, that is, Alice transmits the quantum state to Alice with a certain fidelity, and the fidelity is expressed as:

时，W态可分离；当

时，W态不可分离；当x＝1时，W态为纯态；n表示量子隐形传态的节点数；ρ_in和ρ_n-1分别表示输入量子态以及第n-1个节点的输出量子态的密度算法；Tr表示矩阵的迹。Among them, 0≤x≤1, x represents the weight of the W state in quantum teleportation; when

When , the W state is separable; when

When , the W state is inseparable; when x=1, the W state is a pure state; n represents the number of nodes in quantum teleportation; ρ _in and ρ _n-1 represent the input quantum state and the output of the n-1th node, respectively Density algorithm for quantum states; Tr represents the trace of the matrix.

Specifically, in step S4, the method for Alice and Bob to judge the acquired measurement results is as follows: Alice and Bob each select a part of the key and disclose it, and Alice and Bob calculate the error rate of the key according to the public key , if the error rate exceeds the threshold, the measurement result is judged to be wrong; if the error rate is lower than the threshold, the measurement result is judged to be correct.

Specifically, in step S5, the method of obtaining the sieved key data by operating on the basis is as follows: Alice and Bob first disclose the basis used to prepare each quantum state, and then correspond to the quantum state prepared by using the same basis. The key data of the sieve is retained, and the key data corresponding to the quantum states prepared using different bases is discarded, so as to obtain the sieved key data.

Specifically, in step S7, the method of checking whether there is eavesdropping on the quantum channel is as follows: Alice and Bob both disclose part of the original key, and calculate the bit error rate of the key; if the bit error rate exceeds the threshold, it means that there is eavesdropping, and discard this In the second protocol process, if the bit error rate does not exceed the threshold, the unpublished original key is retained.

Specifically, in step S8, before obtaining the final security key, error correction and encryption amplification operations need to be performed on the remaining key string.

Further, the key rate calculation formula of the protocol is:

f(E_rect)为错误纠正率函数，H(x)＝-xlog₂(x)-(1-x)log₂(1-x)为香农熵函数；

表示在MDI－QKD中斜极化基下的单光子脉冲的错误率；

表示水平垂直基的强度为uv的光脉冲的错误率，u为Alice发送的光脉冲的强度，v为Bob发送的光脉冲的强度。Among them, Q _rect and E _rect represent the gain and quantum bit error rate under the rect basis;

f(E _rect ) is the error correction rate function, H(x)=-xlog ₂ (x)-(1-x)log ₂ (1-x) is the Shannon entropy function;

Indicates the error rate of single-photon pulses in MDI-QKD in the obliquely polarized basis;

It represents the error rate of the optical pulse whose intensity is uv on the horizontal and vertical basis, u is the intensity of the optical pulse sent by Alice, and v is the intensity of the optical pulse sent by Bob.

Further, the gain and quantum bit error rate of the protocol are expressed as:

表示Alice和Bob在rect基下发送强度为u和v的光脉冲的增益；

表示Alice1和Bob在rect基下发送强度为u和v的光脉冲的增益；

表示Alice和Bob在rect基下发送强度为u和v的光脉冲的错误率；

表示Alice1和Bob在rect基下发送强度为u和v的光脉冲的错误率；

表示量子网络中斜极化基的单光子脉冲的错误率，其右上标xx’代表Alice和Bob同时使用斜极化基，该量子网络包括隐形传态和MDI－QKD；表示斜极化基的强度为uv的光脉冲的错误率，其右上标xx代表Alice1和Bob同时使用斜极化基；u为Alice发送的光脉冲的强度；v为Bob发送的光脉冲的强度；Fn表示Alice传送给Alice1的量子态的保真度；在相同纠缠度和密钥率的情况下，随着隐形传态的节点数n的增大，协议的相对传输距离在逐渐减小；在隐形传态的节点数n和密钥率相同的情况下，随着隐形传态时W态的纠缠度的降低，协议的相对传输距离也在逐渐减小。in,

represents the gain of Alice and Bob sending optical pulses with intensities u and v under the rect basis;

Represents the gain of Alice1 and Bob sending optical pulses with intensities u and v under the rect basis;

Represents the error rate of Alice and Bob sending light pulses with intensities u and v under the rect basis;

Represents the error rate of Alice1 and Bob sending light pulses with intensities u and v under the rect basis;

Indicates the error rate of the single-photon pulse of the obliquely polarized base in the quantum network, the superscript xx' on the right represents the simultaneous use of the obliquely polarized base by Alice and Bob, and the quantum network includes teleportation and MDI-QKD; Indicates the error rate of the optical pulse with the intensity of the oblique polarization base as uv, and the right superscript xx represents that Alice1 and Bob use the oblique polarization base at the same time; u is the intensity of the optical pulse sent by Alice; v is the intensity of the optical pulse sent by Bob ; Fn represents the fidelity of the quantum state transmitted by Alice to Alice1; in the case of the same entanglement degree and key rate, as the number of teleportation nodes n increases, the relative transmission distance of the protocol gradually decreases; When the number of nodes n and the key rate of teleportation are the same, with the decrease of the entanglement degree of the W state during teleportation, the relative transmission distance of the protocol is also gradually reduced.

Specifically, the quantum network includes two legitimate communication users Alice and Bob of the quantum network source node, and a quantum network destination node Alice.

Compared with the prior art, the beneficial effects of the present invention are: the communication protocol of the present invention adopts the MDI-QKD protocol, so it has the advantages of the original MDI-QKD protocol, that is, the safety protocol is guaranteed to be independent of the measuring equipment, All attacks on the measuring device end in the QKD system are effectively avoided; the invention applies the quantum teleportation in the quantum network to the MDI-QKD protocol, which greatly improves the distance of the MDI-QKD protocol while ensuring communication security. .

Description of drawings

1 is a flow chart of a quantum network-based MDI-QKD protocol of the present invention;

FIG. 2 is a schematic diagram of a communication network of a quantum network-based MDI-QKD protocol of the present invention.

Detailed ways

The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

As shown in Figure 2, this embodiment provides a quantum network-based MDI-QKD protocol. The protocol in this embodiment mainly includes four parts: the legitimate communication user Alice of the quantum network source node and the destination node of the quantum network destination node Alice1, legal communication user Bob, and third-party measurement equipment; the source node and the destination node are in the same quantum network. The source node and the destination node select an optimal communication line through network routing, and use quantum teleportation to transmit quantum states. Since the distance of quantum cryptographic communication is limited, the distance between Alice and Bob is too far to realize quantum cryptographic communication. The distance between Alice1 and Bob is short, which can realize quantum cryptographic communication independent of measurement equipment. This embodiment shows how to realize the quantum cryptographic communication method between Alice and Bob by means of teleportation technology.

As shown in Figure 1, the specific process of the protocol is as follows:

S1, the legitimate communication user Alice routes an optimal line in the quantum network to the Alice1 node through the quantum intelligent optimization algorithm. There are n intermediate nodes between Alice and Alice1 nodes, and each node will be transmitted through quantum teleportation. way to transmit the quantum state to the Alice1 node;

S2, in the process of quantum teleportation, if the legitimate communication user Alice wants to transmit an unknown quantum state to the node Alice1, firstly, Alice and the nodes near Alice share an entangled quantum channel, that is, the EPR entangled particle pair, and then Alice transfers the original quantum state to the node Alice1. The unknown quantum state is decomposed into classical information and quantum information is transmitted to the intermediate node through the classical channel and quantum channel respectively, and the node restores the unknown quantum state according to the obtained information;

S3, after Alice1 obtains the quantum state transmitted by Alice, and synchronously with another legal communication user Bob, sends their respective quantum states to the third party Charlie through the quantum channel for Bell state measurement;

S4, after the measurement is completed, Charlie announces the measurement result to Alice and Bob through the public channel, and Alice and Bob judge whether the measurement result measured by the Charlie side is the correct result;

S5, if it is judged that the measurement result is wrong, Alice and Bob both discard the quantum state data sent to Charlie for measurement during this communication process; if it is judged that the measurement result is correct, Alice and Bob temporarily retain the quantum state data, and pass the basic After the operation obtains the sieved key data, either Alice or Bob performs a bit flip on its own key;

S6, repeat steps S2 to S5, until obtain enough original key, namely obtain a string of natural key bits;

S7, detect whether there is eavesdropping on the quantum channel;

S8, get the final security key.

Specifically, in step S2, the classical information is the measurement result obtained by the sender Alice performing Bell state measurement on the unknown quantum state to be transmitted, and the quantum information is the rest of the unknown quantum state that Alice did not acquire in the measurement. information. After repeating the teleportation for n-1 times, the quantum state prepared by the legitimate user Alice can be transmitted to the Alice node.

Further, in step S2, the communication user Alice will lose a certain amount of information in the process of transmitting the quantum state, that is, Alice transmits the quantum state to Alice with a certain fidelity, and the fidelity is expressed as:

时，W态可分离；当

时，W态不可分离；当x＝1时，W态为纯态；n表示量子隐形传态的节点数；ρ_in和ρ_n-1分别表示输入量子态以及第n-1个节点的输出量子态的密度算法。Among them, 0≤x≤1, x represents the weight of the W state in quantum teleportation; when

When , the W state is separable; when

When , the W state is inseparable; when x=1, the W state is a pure state; n represents the number of nodes in quantum teleportation; ρ _in and ρ _n-1 represent the input quantum state and the output of the n-1th node, respectively Density algorithm for quantum states.

Specifically, in step S4, the method for Alice and Bob to judge the acquired measurement results is as follows: Alice and Bob each select a part of the key and disclose it, and Alice and Bob calculate the error rate of the key according to the public key , if the error rate exceeds the threshold, the measurement result is judged to be wrong; if the error rate is lower than the threshold, the measurement result is judged to be correct; when the transmission quantum state is a single photon, the threshold is 11%.

Specifically, in step S5, the method of obtaining the sieved key data by operating on the basis is as follows: Alice and Bob first disclose the basis used to prepare each quantum state, and then correspond to the quantum state prepared by using the same basis. The key data of the sieve is retained, and the key data corresponding to the quantum states prepared using different bases is discarded, so as to obtain the sieved key data.

Specifically, in step S7, the method of checking whether there is eavesdropping on the quantum channel is as follows: Alice and Bob both disclose part of the original key, and calculate the bit error rate of the key; if the bit error rate exceeds the threshold, it means that there is eavesdropping, and discard this In the second protocol process, if the bit error rate does not exceed the threshold, the unpublished original key is retained.

Specifically, in step S8, before obtaining the final security key, error correction and encryption amplification operations need to be performed on the remaining key string.

Further, the key rate calculation formula of the original MDI-QKD protocol is:

和可以通过诱骗态的方法估计其值，f(E_rect)＞1为错误纠正率函数，H(x)＝-xlog₂(x)-(1-x)log₂(1-x)为香农熵函数；

表示在MDI－QKD中斜极化基下的单光子脉冲的错误率；

表示水平垂直基的强度为uv的光脉冲的错误率，u为Alice发送的光脉冲的强度，v为Bob发送的光脉冲的强度。Among them, Q _rect and E _rect represent the gain and quantum bit error rate under the rect basis;

and Its value can be estimated by the method of decoy state, f(E _rect )>1 is the error correction rate function, H(x)=-xlog ₂ (x)-(1-x)log ₂ (1-x) is Shannon entropy function;

Indicates the error rate of single-photon pulses in MDI-QKD in the obliquely polarized basis;

It represents the error rate of the optical pulse whose intensity is uv on the horizontal and vertical basis, u is the intensity of the optical pulse sent by Alice, and v is the intensity of the optical pulse sent by Bob.

When Alice1 and Bob are preparing phase-randomized weak correlation pulses (WCP), and there is no eavesdropper in the communication process, the total gain and QBER can be written in the following form:

和

分别表示正确和错误贝尔态测量下的增益，I₀(·)是一阶修正贝塞尔函数，e_d是误差率，p_d是暗计数率，e₀＝1/2，ω＝μη_α+νη_b，

y＝(1-p_d)e^-ω/4，η_α＝η_b＝10^-αL/10为信道的传输效率。in,

and

are the gains under correct and incorrect Bell state measurements, respectively, I ₀ (·) is the first-order modified Bessel function, _{ed is the error rate, p d is} the dark count rate, e ₀ =1/2, ω = μη _α +νη _b ,

y=(1-p _d )e ^-ω/4 , η _α =η _b =10 ^-αL/10 is the transmission efficiency of the channel.

Further, combined with the fidelity in the quantum teleportation process, the gain and quantum bit error rate of the quantum network-based MDI-QKD protocol can be expressed as:

表示Alice和Bob在rect基下发送强度为u和v的光脉冲的增益；表示Alice1和Bob在rect基下发送强度为u和v的光脉冲的增益；

表示Alice和Bob在rect基下发送强度为u和v的光脉冲的错误率；

表示Alice1和Bob在rect基下发送强度为u和v的光脉冲的错误率；

表示量子网络中斜极化基的单光子脉冲的错误率，其右上标xx’代表Alice和Bob同时使用斜极化基，该量子网络包括隐形传态和MDI－QKD；

表示斜极化基的强度为uv的光脉冲的错误率，其右上标xx代表Alice1和Bob同时使用斜极化基；u为Alice发送的光脉冲的强度；v为Bob发送的光脉冲的强度；Fn表示Alice传送给Alice1的量子态的保真度；由上述公式可以看出，针对于量子隐形传态中的保真度Fn，隐形传态数目n及纠缠度会影响该协议的性能。在相同纠缠度和密钥率的情况下，随着隐形传态的节点数n的增大，协议的相对传输距离在逐渐减小；在隐形传态的节点数n和密钥率相同的情况下，随着隐形传态时W态的纠缠度的降低，协议的相对传输距离也在逐渐减小。in,

represents the gain of Alice and Bob sending optical pulses with intensities u and v under the rect basis; Represents the gain of Alice1 and Bob sending optical pulses with intensities u and v under the rect basis;

Represents the error rate of Alice and Bob sending light pulses with intensities u and v under the rect basis;

Represents the error rate of Alice1 and Bob sending light pulses with intensities u and v under the rect basis;

Indicates the error rate of the single-photon pulse of the obliquely polarized base in the quantum network, the superscript xx' on the right represents the simultaneous use of the obliquely polarized base by Alice and Bob, and the quantum network includes teleportation and MDI-QKD;

Indicates the error rate of the optical pulse with the intensity of the oblique polarization base as uv, and the right superscript xx represents that Alice1 and Bob use the oblique polarization base at the same time; u is the intensity of the optical pulse sent by Alice; v is the intensity of the optical pulse sent by Bob ; Fn represents the fidelity of the quantum state transmitted by Alice to Alice1; it can be seen from the above formula that for the fidelity Fn in quantum teleportation, the number of teleportation states n and the degree of entanglement will affect the performance of the protocol. In the case of the same entanglement degree and key rate, as the number of teleportation nodes n increases, the relative transmission distance of the protocol gradually decreases; when the number of teleportation nodes n and the key rate are the same As the entanglement degree of the W state decreases during teleportation, the relative transmission distance of the protocol also decreases gradually.

After the quantum teleportation in the quantum network is applied to the MDI-QKD protocol, the invention can greatly improve the safe communication distance of the legal communication users of the MDI-QKD protocol under the condition of less sacrifice of the key rate.

Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.

Claims (8)

1. An MDI-QKD method based on a quantum network is characterized by comprising the following steps:

s1, the communication user Alice establishes an optimal routing route by the method of quantum routing and the node Alicel in the same quantum network;

s2, communication users Alice and Bob in the same quantum network respectively prepare quantum states, and the communication users Alice transmit the prepared quantum states to a node Alicel in a hidden state transmission mode;

s3, after receiving the quantum state, Alicel sends the two quantum states to third-party quantum measurement equipment Charlie through a quantum channel synchronously with Bob for measurement;

s4, Charlie carries out BELL state measurement on the two received quantum states, and then publishes the measurement result to communication users Alice and Bob through a classical channel; the obtained measurement results are judged by Alice and Bob;

s5, if the measurement result is judged to be wrong, then both Alice and Bob discard the quantum state data sent to Charlie measurement in the communication process; if the measurement result is judged to be correct, then Alice and Bob temporarily reserve the quantum state data, and obtain the screened key data through the base pair operation, and either Alice or Bob performs one-time bit reversal on the own key;

s6, repeating the steps S2 to S5 to obtain a string of key bits;

s7, detecting whether the quantum channel has wiretap, if yes, abandoning the protocol process; if there is no eavesdropping, go to step S8;

and S8, obtaining the final security key through error correction and secret amplification.

2. The quantum-network-based MDI-QKD method according to claim 1, wherein in step S2, said communication user Alice loses a certain amount of information in the process of transferring quantum states, that is, there is a certain fidelity in transferring quantum states to Alicel by Alice, said fidelity is expressed as:

wherein x is more than or equal to 0 and less than or equal to 1, and x represents the weight of the W state in the quantum invisible state; when in use

Then, the W state can be separated; when in use

When the temperature of the water is higher than the set temperature,the W state can not be separated; when x is 1, the W state is a pure state; n represents the node number of the quantum invisible state; rho_inAnd ρ_n-1Density algorithms representing input quantum states and output quantum states of the (n-1) th node, respectively; tr denotes the traces of the matrix.

3. The quantum-network-based MDI-QKD method according to claim 1, wherein in step S4, the method for Alice and Bob to determine the obtained measurement results comprises: respectively selecting and disclosing a part of secret keys by Alice and Bob, calculating the error rate of the secret keys by the Alice and the Bob according to the public secret keys, and judging that the measurement result is wrong if the error rate exceeds a threshold value; and if the error rate is lower than the threshold value, judging that the measurement result is correct.

4. The quantum-network-based MDI-QKD method according to claim 1, wherein in step S5, said method for obtaining the filtered key data by the base-pair operation is: and firstly disclosing bases used for preparing each quantum state by Alice and Bob, then reserving key data corresponding to the quantum states prepared by using the same base, and discarding the key data corresponding to the quantum states prepared by using different bases, thereby obtaining the screened key data.

5. The quantum network-based MDI-QKD method according to claim 1, wherein in step S7, the method for checking whether there is eavesdropping on the quantum channel is: both Alice and Bob publicly show part of the original secret key, and calculate the error rate of the secret key; if the error rate exceeds the threshold, it shows that there is eavesdropping, abandon the protocol process, if the error rate does not exceed the threshold, then keep the original key not disclosed.

6. The quantum-network-based MDI-QKD method according to claim 1, wherein the key rate calculation formula of said protocol is:

wherein Q is_rectAnd E_rectRepresenting the gain and the quantum bit error rate under the rect base;

f(E_rect) H (x) xlog as a function of error correction rate₂(x)-(1-x)log₂(1-x) is a Shannon entropy function;

represents the error rate of a single-photon pulse under the oblique polarization base in MDI-QKD;indicating the error rate of the optical pulses with the intensity of the horizontal and vertical basis uv, u being the intensity of the optical pulses transmitted by Alice and v being the intensity of the optical pulses transmitted by Bob.

7. The quantum network-based MDI-QKD method according to claim 1, wherein the gain and quantum bit error rate of said protocol are expressed as:

wherein,

represents the sending intensity of Alice and Bob under rect baseThe gain of the optical pulse at u and v;

represents the gain at which Alice1 and Bob send optical pulses of intensities u and v on the rect basis;representing the error rate of sending light pulses with the intensity u and v by Alice and Bob under the rect base;

representing the error rate of Alice1 and Bob sending light pulses of intensities u and v on the rect basis;

representing the error rate of single-photon pulses of an oblique polarization base in a quantum network, wherein the upper right label xx' represents that Alice and Bob use the oblique polarization base simultaneously, and the quantum network comprises an invisible state and MDI-QKD;

indicating the error rate of the optical pulse with the intensity uv of the oblique polarization base, and the upper right label xx represents that Alice1 and Bob use the oblique polarization base simultaneously; u is the intensity of the optical pulse transmitted by Alice; v is the intensity of the light pulse sent by Bob; fn represents the fidelity of the quantum states communicated by Alice to Alice 1; under the condition of the same entanglement and key rate, the relative transmission distance of the protocol is gradually reduced along with the increase of the number n of nodes in the invisible transmission state; under the condition that the number n of nodes in the invisible transmission state is the same as the key rate, the relative transmission distance of the protocol is gradually reduced along with the reduction of the entanglement degree of the W state in the invisible transmission state.

8. The quantum network-based MDI-QKD method according to claim 1, wherein the quantum network comprises two legal communication users Alice and Bob of source nodes of the quantum network and one destination node Alicel of the quantum network.

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