A method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint

Abstract

The present invention relates to a method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control, comprising establishing a quantum entanglement channel based on a first sender Alice1, a second sender Alice2, a receiver Bob and a plurality of intermediate nodes; there is a dislocation in the channel between Bob and the intermediate node; the intermediate node performs Bell measurement on a particle pair carried by itself, and sends the Bell measurement result and dislocation information to Bob; so that Bob constructs a dislocation matrix, performs dislocation correction, and determines a direct entanglement channel; Bob performs corresponding unitary operations on the particles carried by itself according to the format of the direct entanglement channel; Alice1 performs CNOT operation and single-particle measurement on its particle pair, and then performs POVM measurement, obtains a single-particle measurement result containing amplitude information of a quantum state to be prepared and a POVM measurement result, and sends them to Bob; Alice2 performs projection measurement on the particles carried by it, obtains a projection measurement result containing phase information of the quantum state to be prepared, and sends it to Bob; Bob performs corresponding unitary operations on the particles carried by it according to multiple measurement results, and recovers the quantum state to be prepared.

Description

Technical Field

[0001] The present invention relates to the field of communication network and information dissemination technology, and in particular to a method for remotely preparing quantum states based on bidirectional fault-tolerant multi-hop joint. Background Art

[0002] With the development of society and the progress of science and technology, information technology has made unprecedented breakthroughs. Information, matter and energy have become the basic elements for the existence and development of today's society. Information theory and quantum theory are two important discoveries of the 20th century. With the continuous deepening of research, in the last twenty years of the last century, they began to cross and merge, and then produced quantum information science based on quantum mechanics. Quantum information science is an emerging frontier science that studies information processing based on the principle of superposition of quantum mechanics. It includes quantum cryptography, quantum communication, quantum algorithms and quantum computers. In recent years, it has made major breakthroughs in theory and experiment.

[0003] Quantum teleportation restores the unknown state of the bit held by one party to the bit held by the other party, without the need for the sender to directly transmit the physical bit carrying the unknown information to the receiver, thus almost realizing the transmission of information in hyperspace. In 1993, Bennett et al. first proposed the transmission of unknown quantum states by classical channels and EPR channels. Since Bennett et al. proposed the initial scheme, it has attracted widespread attention due to its wonderful properties, and has made positive progress in both theory and experiment. Over the past few decades, in order to meet various quantum communication scenarios, a series of quantum teleportation protocols involving different quantum channels have been proposed, such as Bell states, GHZ states, and W states. At the same time, many experimental schemes have also been proposed, such as cavity quantum electrodynamics, ion traps, quantum dots, optics, and nuclear magnetic resonance.

[0004] However, due to the inevitable loss of quantum channels, it is unrealistic to directly transmit quantum states between two distant nodes. In order to overcome this limitation, quantum communication is gradually moving towards the direction of network development. Quantum networks are based on point-to-point quantum key distribution, which enables the communicating parties in the network to exchange theoretically secure keys, rather than infrastructure for secure communication. Quantum networks contain multiple intermediate nodes and adjacent nodes share a pair of entangled sources. Through entanglement exchange, communication between two distant nodes is finally achieved. Compared with classical communication networks, quantum communication networks have several significant advantages: higher security and confidentiality of communication; stronger information transmission and processing capabilities make communication more efficient; and lower communication complexity. At present, many research groups have proposed their own ideas for building quantum networks. In 2014, Wang et al. proposed a quantum wireless multi-hop teleportation method based on Bell pairs to build a quantum communication network. In 2017, in order to improve transmission efficiency, Zou et al. proposed a multi-hop teleportation protocol to achieve quantum teleportation of unknown two-particle states through a composite GHZ-Bell channel. Recently, Zhou et al. proposed a multi-hop teleportation scheme, using W states as quantum channels for transmission. After Lo and Pati proposed the remote state preparation scheme, due to the advantage of RSP in reducing the consumption of classical information and quantum resources, many remote state preparation schemes have emerged, including bidirectional quantum state preparation, controlled quantum state preparation, and multi-party quantum state remote preparation. In 2012, Zhan et al. proposed an improved scheme that cleverly used a new unitary operation to realize the preparation of arbitrary two-bit and three-bit quantum states with a success rate of 100%. In 2019, Zhang et al. proposed a JRSP scheme for mixed states using three-qubit GHZ states. The success probability of this scheme is deterministic for real coefficient mixed states and probabilistic for complex coefficients.

[0005] Moreover, in actual quantum communication networks, due to the interaction between particles and the environment, their quantum states will be affected by quantum noise and change during channel transmission. The following types of quantum bit dislocations may occur when a quantum bit interacts with the environment: I-no error; X-bit reversal error; Z-bit phase error; XZ-bit reversal error + bit phase error. Based on this, quantum communication networks need to use quantum error correction technology to ensure the reliable transmission of the original unknown quantum state information. It protects the quantum channel based on the principles of quantum mechanics and can ensure the absolute reliability of communication between two places. Summary of the invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problems of low information transmission efficiency and inability to achieve bidirectional fault tolerance in the prior art.

[0007] In order to solve the above technical problems, the present invention provides a method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint, comprising:

[0008] A quantum entanglement channel is established based on a first sender Alice1, a second sender Alice2, a receiver Bob and a plurality of intermediate nodes; a channel between the receiver Bob and the intermediate nodes has a dislocation;

[0009] The intermediate node performs Bell measurement on the particle pair it carries, and sends the Bell measurement result and the bit error information to the receiver Bob;

[0010] The receiver Bob constructs the error matrix according to the error information of each intermediate node, performs error correction operation, and determines the direct entanglement channel according to the error information and Bell measurement results;

[0011] The receiver Bob performs corresponding unitary operations on the particles he carries according to the format of the direct entanglement channel;

[0012] After the first sender Alice1 performs a CNOT operation on its particle pair, it performs a single-particle measurement on the target quantum bit and a POVM measurement on the control quantum bit, obtains the single-particle measurement result containing the amplitude information of the quantum state to be prepared and the POVM measurement result, and sends them to the receiver Bob;

[0013] The second sender Alice2 performs projection measurement on the particles it carries, obtains the projection measurement results containing the phase information of the quantum state to be prepared, and sends them to the receiver Bob;

[0014] The receiver Bob performs corresponding unitary operations on the particles it carries according to the single-particle measurement result, the POVM measurement result and the projection measurement result to restore the quantum state to be prepared.

[0015] In one embodiment of the present invention, the step of establishing a quantum entanglement channel based on a first sender Alice1, a second sender Alice2, a receiver Bob and a plurality of intermediate nodes includes:

[0016] The first sender Alice1, the second sender Alice2, the receiver Bob and multiple intermediate nodes are connected in pairs through non-maximum entanglement Bell channels, and the non-maximum entanglement Bell channels are expressed as:

[0017]

[0018] Among them, the coefficients a0 and a1 are real numbers and meet the normalization conditions: The first sender Alice1 holds the amplitude information of the quantum state to be prepared, and has the target quantum bit A1 and the control quantum bit P1; the second sender Alice2 holds the phase information of the quantum state to be prepared, and has the particle p2; the receiver Bob has the particle B q+1 ; The kth intermediate node has particle pair A k ,B k (k=1,2,…,q+1); quantum states will produce dislocations during channel transmission, and channel bits will flip due to environmental interference. Typical flips are I, X, Z, and XZ. Assume that A in the kth node k ,B k (k=1,2,…,q+1) particle pairs are dislocated, that is, both ends of the Bell channel are flipped, and the dislocation information is e fg =Z f X g , where f,g=0,1;

[0019] The quantum entangled channel, that is, the initial state of the system can be expressed as:

[0020]

[0021] In one embodiment of the present invention, the particle pair A of the intermediate node in the initial state of the system k ,B k The joint system state composed of (k=1,2,...,q+1) is expressed as:

[0022]

[0023] Among them, |φ uv > where u and v are 0 and 1 combinations, expressed as:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] m (k) ,n (k) represents the Bell measurement result of the kth intermediate node particle pair; represents XOR, represents AND operation; U cor The constructed dislocation matrix is ​​expressed as

[0032] In one embodiment of the present invention, the direct entanglement channel is expressed as:

[0033]

[0034] Among them, the coefficients b0 and b1 are expressed as:

[0035]

[0036]

[0037] In one embodiment of the present invention, the joint system state of the intermediate node particle pair in the direct entanglement channel is expressed as:

[0038]

[0039] In one embodiment of the present invention, the receiver Bob performs corresponding unitary operations on the particles carried by himself according to the format of the direct entanglement channel, including:

[0040] When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=I=|0><0|+|1><1|;

[0041] When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=X=|0><1|+|1><0|;

[0042] When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=Z=|0><0|-|1><1|;

[0043] When the direct entanglement channel is When the particle B of the receiver Bob q+1 A unitary operation U=ZX=(0><0|-|1><1|)(0><1|+|1><0|) is performed.

[0044] In one embodiment of the present invention, after the first sender Alice1 performs a CNOT operation on its particle pair, it performs a single-particle measurement on the target quantum bit, performs a POVM measurement on the control quantum bit, obtains a single-particle measurement result containing the amplitude information of the quantum state to be prepared and a POVM measurement result and sends them to the receiver Bob, including:

[0045] The first sender Alice1 performs a CNOT operation on its particle pair (P1, A1) and performs a single-particle measurement on particle A1 with a basis of {|t>, t=0, 1};

[0046] The first sender Alice1 performs POVM measurement on particle P1, expressed as:

[0047]

[0048]

[0049] in, The coefficient x satisfies

[0050] In one embodiment of the present invention, after the first sender Alice1 performs a CNOT operation on its particle pair (P1, A1), the joint system state of the intermediate node particle pair is expressed as:

[0051]

[0052] Among them, redefinition The joint system state is expressed as:

[0053]

[0054] In one embodiment of the present invention, the second sender Alice2 performs projection measurement on the particles it carries, obtains the projection measurement result containing the phase information of the quantum state to be prepared, and sends it to the receiver Bob, including:

[0055] After the receiver Bob obtains the projection measurement result, he selects the preset phase measurement basis | n >(n=0,1) is:

[0056]

[0057] In one embodiment of the present invention, the receiver Bob performs corresponding unitary operations on the particles it carries according to the single-particle measurement result, the POVM measurement result and the projection measurement result to restore the quantum state to be prepared, including:

[0058] The receiver Bob measures particle B based on the single particle measurement result.q+1 The first unitary operation performed is expressed as:

[0059]

[0060] The receiver Bob calculates the B after the first unitary operation based on the POVM measurement result and the projection measurement result. q+1 Perform the second unitary operation to restore the quantum state to be prepared include:

[0061] If the POVM measurement result is |P0> and the projection measurement result is |O0>, then the second unitary operation is performed.

[0062] If the POVM measurement result is |P0> and the projection measurement result is |O1>, the second unitary operation is performed.

[0063] If the POVM measurement result is |P1> and the projection measurement result is |O0>, then the second unitary operation is performed.

[0064] If the POVM measurement result is |P1> and the projection measurement result is |O1>, then the second unitary operation is performed

[0065] If the POVM measurement result is |P2>, the preparation failure is returned.

[0066] The above technical solution of the present invention has the following advantages compared with the prior art:

[0067] The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control described in the present invention constructs a multi-hop quantum network composed of multiple intermediate nodes between the first sender Alice1, the second sender Alice2 and the receiver Bob. The multiple intermediate nodes can perform Bell measurements at the same time, and send the measurement results and dislocation information to the receiver Bob at the same time, thereby improving the efficiency of information transmission; and the multi-hop quantum network solves the problem of long-distance remote quantum state preparation, and can meet the needs of building complex quantum networks. The present invention uses the particle pairs of multiple intermediate nodes to directly send the dislocation information generated by the quantum bit to the receiver. The receiver Bob performs corresponding unitary transformation on the particles it carries according to the obtained measurement results and dislocation information, corrects quantum errors, realizes bidirectional fault tolerance, and correctly recovers the quantum state to be prepared; and the error correction operation and the recovery operation of the quantum state to be prepared are both performed by the receiver Bob, which simplifies the operation of the intermediate party and improves the transmission efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0069] Figure 1 It is a schematic diagram of the steps of the method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint provided by the present invention;

[0070] Figure 2 It is a schematic diagram of particle allocation of a method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint in a single intermediate node provided by an embodiment of the present invention;

[0071] Figure 3 It is a quantum circuit diagram of a method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint in a single intermediate node provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0073] The present invention proposes a method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint. Through channel error correction technology, each communication node on the communication path directly sends the errors generated by the quantum bit to the information receiver, and the information receiver then performs appropriate matrix transformation to correct the quantum error and correctly recover the transmitted unknown quantum state information.

[0074] Reference Figure 1 As shown, the method of the present invention based on bidirectional fault-tolerant multi-hop joint remote preparation of quantum states includes:

[0075] S101: establishing a quantum entanglement channel based on a first sender Alice1, a second sender Alice2, a receiver Bob and a plurality of intermediate nodes; a channel between the receiver Bob and the intermediate nodes has a dislocation;

[0076] The first sender Alice1, the second sender Alice2 and the receiver Bob are in a multi-hop quantum network. Alice1 and Alice2 hold the amplitude information and phase information of the quantum state to be prepared respectively, and jointly prepare any single-bit quantum state for the receiver Bob remotely. where α0,α1∈R, and |α0| 2 +|α1| 2 =1,λ1∈[0,2π); Alice1 holds the amplitude information and Alice2 holds the phase information;

[0077] The first sender Alice1, the second sender Alice2, the receiver Bob and multiple intermediate nodes are connected in pairs through non-maximum entanglement Bell channels, and the non-maximum entanglement Bell channels are expressed as:

[0078]

[0079] Among them, the coefficients a0 and a1 are real numbers and meet the normalization conditions: The first sender Alice1 holds the amplitude information of the quantum state to be prepared, and has the target quantum bit A1 and the control quantum bit P1; the second sender Alice2 holds the phase information of the quantum state to be prepared, and has the particle p2; the receiver Bob has the particle B q+1 ; The kth intermediate node has particle pair A k ,B k (k=1,2,…,q+1); quantum states will produce dislocations during channel transmission, and channel bits will flip due to environmental interference. Typical flips are I, X, Z, and XZ. Assume that A in the kth node k ,B k (k=1,2,…,q+1) particle pairs are dislocated, that is, both ends of the Bell channel are flipped, and the dislocation information is e fg =Z f X g , where f,g=0,1;

[0080] The quantum entangled channel, that is, the initial state of the system can be expressed as:

[0081]

[0082] In the initial state of the system, the particle pair A of the intermediate node k ,B k The joint system state composed of (k=1,2,…,q+1) is expressed as:

[0083]

[0084] Among them, |φ uv > where u and v are 0 and 1 combinations, expressed as:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] m (k) ,n (k) represents the Bell measurement result of the kth intermediate node particle pair; represents XOR, represents AND operation; U cor The constructed dislocation matrix is ​​expressed as

[0093] S102: The intermediate node performs Bell measurement on the particle pair it carries, and sends the Bell measurement result and the bit error information to the receiver Bob;

[0094] S103: The receiver Bob constructs a dislocation matrix based on the dislocation information of each intermediate node, performs a dislocation correction operation, and determines the direct entanglement channel based on the dislocation information and Bell measurement results;

[0095] The direct entanglement channel is expressed as:

[0096]

[0097] Among them, the coefficients b0 and b1 are expressed as:

[0098]

[0099]

[0100] The joint system state of the intermediate node particle pair under the direct entanglement channel is expressed as:

[0101]

[0102] S104: The receiver Bob performs corresponding unitary operations on the particles he carries according to the format of the direct entanglement channel;

[0103] When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=I=|0><0|+|1><1|;

[0104] When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=X=|0><1|+|1><0|;

[0105] When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=Z=|0><0|-|1><1|;

[0106] When the direct entanglement channel is When the particle B of the receiver Bob q+1 A unitary operation U=ZX=(|0><0|-|1><1|)(0><1|+|1><0|) is performed.

[0107] S105: After the first sender Alice1 performs a CNOT operation on its particle pair, it performs a single-particle measurement on the target quantum bit and a POVM measurement on the control quantum bit, obtains a single-particle measurement result containing the amplitude information of the quantum state to be prepared and a POVM measurement result, and sends them to the receiver Bob;

[0108] The first sender Alice1 performs a CNOT operation on its particle pair (P1, A1) and performs a single-particle measurement on particle A1 with a basis of {|t>, t=0, 1};

[0109] The first sender Alice1 performs POVM measurement on particle P1, expressed as:

[0110]

[0111]

[0112] in, The coefficient x satisfies

[0113] After performing the CNOT operation, the joint system state of the intermediate node particle pair is expressed as:

[0114]

[0115] Among them, redefinition After that, the joint system state is expressed as:

[0116]

[0117] S106: The second sender Alice2 performs projection measurement on the particles it carries, obtains the projection measurement result containing the phase information of the quantum state to be prepared, and sends it to the receiver Bob;

[0118] After the receiver Bob obtains the projection measurement result, he selects the preset phase measurement basis | n >(n=0,1) is:

[0119]

[0120] S107: The receiver Bob performs corresponding unitary operations on the particles he carries according to the single-particle measurement result, the POVM measurement result and the projection measurement result to restore the quantum state to be prepared.

[0121] The receiver Bob measures particle B based on the single particle measurement result. q+1 The first unitary operation performed is expressed as:

[0122]

[0123] The receiver Bob calculates the B after the first unitary operation based on the POVM measurement result and the projection measurement result. q+1 Perform the second unitary operation to restore the quantum state to be prepared include:

[0124] If the POVM measurement result is |P0> and the projection measurement result is |O0>, then the second unitary operation is performed.

[0125] If the POVM measurement result is |P0> and the projection measurement result is |O1>, the second unitary operation is performed.

[0126] If the POVM measurement result is |P1> and the projection measurement result is |O0>, then the second unitary operation is performed.

[0127] If the POVM measurement result is |P1> and the projection measurement result is |O1>, then the second unitary operation is performed

[0128] If the POVM measurement result is |P2>, the preparation failure is returned.

[0129] Specifically, in the present invention, the quantum state of any single-bit state to be prepared is expressed as:

[0130]

[0131] The Bell basis is the maximum entangled state composed of two particles. It constitutes a set of complete orthogonal bases in the four-dimensional Hilbert space. The specific form is as follows:

[0132]

[0133]

[0134] The controlled NOT gate (CNOT) has two input qubits, namely the control qubit and the target qubit. Its function is: when the control qubit state is |0>, the target qubit state remains unchanged; when the control qubit state is |1>, the target qubit state is flipped from |0> to |1>, or from |1> to >0>. Its corresponding matrix form is:

[0135]

[0136] Unitary matrix, also known as Pauli matrix. The specific form is as follows:

[0137]

[0138]

[0139] The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control described in the present invention constructs a multi-hop quantum network composed of multiple intermediate nodes between the first sender Alice1, the second sender Alice2 and the receiver Bob. The multiple intermediate nodes can perform Bell measurements at the same time, and send the measurement results and dislocation information to the receiver Bob at the same time, thereby improving the efficiency of information transmission; and the multi-hop quantum network solves the problem of long-distance remote quantum state preparation, and can meet the needs of building complex quantum networks. The present invention uses the particle pairs of multiple intermediate nodes to directly send the dislocation information generated by the quantum bit to the receiver. The receiver Bob performs corresponding unitary transformation on the particles it carries according to the obtained measurement results and dislocation information, corrects quantum errors, realizes bidirectional fault tolerance, and correctly recovers the quantum state to be prepared; and the error correction operation and the recovery operation of the quantum state to be prepared are both performed by the receiver Bob, which simplifies the operation of the intermediate party and improves the transmission efficiency.

[0140] Based on the above embodiment, in this embodiment, based on a single intermediate node, the above method for remote preparation of quantum states based on bidirectional fault-tolerant multi-hop joint is implemented, including:

[0141] S201: establishing a quantum entanglement channel based on a first sender Alice1, a second sender Alice2, a receiver Bob and a plurality of intermediate nodes; a channel between the receiver Bob and the intermediate nodes has a dislocation;

[0142] The senders Alice1, Alice2 and the receiver Bob are in a multi-hop quantum network. Alice1 and Alice2 hold the amplitude and phase information of the quantum state to be prepared respectively, and jointly prepare any single-bit state for the receiver Bob remotely. Alice1 holds the amplitude information and Alice2 holds the phase information.

[0143] Reference Figure 2 As shown in the figure, there is an intermediate node on the path between the sender and the receiver, and a quantum entanglement channel is established between Alice1, Alice2, Bob and the intermediate node; on the transmission path, Alice1, Alice2, Bob and the intermediate node are connected to each other through a non-maximum entanglement Bell channel. The form of the non-maximum entanglement Bell channel is as follows:

[0144]

[0145] The coefficients a0 and a1 are real numbers and satisfy the normalization condition: a1 2 +a1 2 = 1. Alice1 has particles A1, p1, Alice2 has particle p2, Bob has particle B2, and the intermediate node has particles B1, A2. The channel generates a bit error during transmission. Assume that particles A1, A2, B1, B2 are flipped, and the bit error information is e fg =Z f X g , where f,g=0,1; the initial state of the system can be written as:

[0146]

[0147] In the initial state of the system, particle A k ,B k The joint system state composed of (k=1,2,…q+1) can be written as:

[0148]

[0149] The above formula can be further rewritten as:

[0150]

[0151] Here | φ uv > where u and v are a combination of 0 and 1, which is as follows:

[0152]

[0153] in,

[0154]

[0155]

[0156]

[0157]

[0158] L 00 =m·n;

[0159] In the above formula, m and n represent the Bell measurement results of the intermediate node particle pair; the symbol “” and “-” represent XOR, AND, and NOT operations respectively; Bob constructs the dislocation matrix U according to the dislocation information published by each intermediate node. cor for:

[0160]

[0161] S202: The intermediate node performs Bell measurement on the particle pair it carries, and sends the Bell measurement result and the bit error information to the receiver Bob;

[0162] S203: The receiver Bob constructs a dislocation matrix based on the dislocation information of each intermediate node, performs dislocation correction operations, and determines the direct entanglement channel based on the dislocation information and Bell measurement results.

[0163] For the convenience of analysis, the coefficients are redefined as follows:

[0164]

[0165] Therefore, the direct entanglement channel between Alice1 and Bob is:

[0166]

[0167] At this time, the joint system state is expressed as:

[0168]

[0169] S204: The receiver Bob performs corresponding unitary operations on the particle B2 carried by himself according to the format of the direct entanglement channel;

[0170] The corresponding unitary operation is shown in Table 1:

[0171] Table 1: Unitary operations corresponding to the direct entanglement channel format

[0172]

[0173] S205: After the first sender Alice1 performs a CNOT operation on its particle pair (p1, A1), it performs a single-particle measurement on the target quantum bit and a POVM measurement on the control quantum bit, obtains a single-particle measurement result containing the amplitude information of the quantum state to be prepared and a POVM measurement result, and sends them to the receiver Bob;

[0174] Alice1 performs a single-particle measurement on its particle A1 with a basis of {|t>, t=0,1}, and sends the single-particle measurement result to Bob;

[0175] To prepare the amplitude information, Alice1 performs a POVM measurement on particle p1 in the form:

[0176]

[0177] in, To ensure that all diagonal elements in P2 are non-negative, the minimum value of the coefficient x needs to satisfy

[0178] At this time, the joint system state of the intermediate node particle pair is expressed as:

[0179]

[0180] Among them, redefinition After that, the joint system state is expressed as:

[0181]

[0182] S206: The second sender Alice2 performs projection measurement on the particles it carries, obtains the projection measurement result containing the phase information of the quantum state to be prepared, and sends it to the receiver Bob;

[0183] In order to prepare the phase information, Bob selects the corresponding phase measurement basis according to the information he has. n >(n=0,1) is:

[0184]

[0185] S207: The receiver Bob performs corresponding unitary operations on the particles he carries according to the single-particle measurement result, the POVM measurement result and the projection measurement result to restore the quantum state to be prepared.

[0186] S207-1: The receiver Bob performs the first unitary operation on particle B2 according to the single particle measurement result, which is expressed as:

[0187]

[0188] S207-2: The receiver Bob performs the first unitary operation on B according to the POVM measurement result and the projection measurement result. q+1 Perform the second unitary operation; refer to Table 2, which shows the unitary operation corresponding to the measurement result:

[0189] Table 2: Unitary operations corresponding to measurement results

[0190]

[0191] As can be seen from the above table, when Alice1's POVM measurement result is |P0> or |P1>, the accepting user Bob executes the corresponding U on his B2 particle. l Operation can restore the target state When Alice2's POVM measurement result is |P2>, it will be difficult for the receiving user Bob to determine what quantum state particle B2 is in, which will cause the remote state preparation scheme to fail;

[0192] Ignoring the global phase, when Alice1's POVM measurement result for particle p1 is |P0>, |P1>, it is determined that the receiving user needs to perform U on the particle B2 he holds. l Operation, Bob can recover to the state to be prepared

[0193]

[0194] Specifically, refer to Figure 3 As shown, in an embodiment of the present invention, a projection measurement PM is performed on the particle P2 of the second receiver Alice2, a CNOT operation is performed on the particle pair (P1, A1) of the first receiver Alice1, and a single particle measurement SM is performed on the particle A1, and a POVN measurement is performed on the particle P1; a Bell measurement BM is performed on the intermediate node particle pair (B1, A2), and through the Bell measurement result U, the projection measurement result U1, the single particle measurement result U' and the POVM measurement result U1, at the receiver Bob, an error correction operation is performed on the particle B2 and the quantum state to be prepared is recovered, thereby realizing remote preparation of the quantum state.

[0195] In the method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control provided by the present invention, both the error correction operation and the original unknown quantum state recovery operation are uniformly performed by the receiver Bob, thereby simplifying the operation of the intermediate party; in the present invention, each node on the communication path can perform Bell measurement at the same time, and simultaneously send the dislocation information and the Bell measurement result to the receiver Bob, thereby improving the efficiency of information transmission; the present invention solves the problem of long-distance remote quantum state preparation through a multi-hop network, and can meet the needs of building a complex quantum network. By utilizing each communication node on the communication path, the error generated by the quantum bit is directly sent to the information receiver Bob, and the information receiver Bob thereby performs a suitable matrix transformation to correct the quantum error, thereby correctly recovering the transmitted unknown quantum state information and realizing the preparation of the quantum state.

[0196] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0197] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0198] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0199] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0200] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A method for preparing quantum states remotely based on bidirectional fault-tolerant multi-hop joint, characterized in that: include: A quantum entangled channel is established based on the first sender Alice1, the second sender Alice2, the receiver Bob and multiple intermediate nodes, which are connected in pairs through non-maximum entangled Bell channels, expressed as: Among them, the coefficients a0 and a1 are real numbers and meet the normalization conditions: The first sender Alice1 holds the amplitude information of the quantum state to be prepared, and has the target quantum bit A1 and the control quantum bit p1; the second sender Alice2 holds the phase information of the quantum state to be prepared, and has the particle p2; the receiver Bob has the particle B q+1 ; The kth intermediate node has particle pair A k ,B k (k=1,2,…,q+1); quantum states will produce dislocations during channel transmission, and channel bits will flip due to environmental interference. Typical flips are I, X, Z, and XZ. Assume that A in the kth node k ,B k (k=1,2,…,q+1) particle pairs are dislocated, that is, both ends of the Bell channel are flipped, and the dislocation information is e fg =Z f X g , where f,g=0,1; The quantum entangled channel, that is, the initial state of the system can be expressed as: There is a bit error in the channel between the receiver Bob and the intermediate node; The particle pair A of the intermediate node in the initial state of the system k ,B k The joint system state composed of (k=1,2,…,q+1) is expressed as: Among them, |φ uv > where u and v are 0 and 1 combinations, expressed as: m (k) ,n (k) represents the Bell measurement result of the kth intermediate node particle pair; represents XOR, represents AND operation; U cor The constructed dislocation matrix is ​​expressed as The intermediate node performs Bell measurement on the particle pair it carries, and sends the Bell measurement result and the bit error information to the receiver Bob; The receiver Bob constructs the error matrix according to the error information of each intermediate node, performs error correction operation, and determines the direct entanglement channel according to the error information and Bell measurement results; The receiver Bob performs corresponding unitary operations on the particles he carries according to the format of the direct entanglement channel; After the first sender Alice1 performs a CNOT operation on its particle pair, it performs a single-particle measurement on the target quantum bit and a POVM measurement on the control quantum bit, obtains the single-particle measurement result containing the amplitude information of the quantum state to be prepared and the POVM measurement result, and sends them to the receiver Bob; The second sender Alice2 performs projection measurement on the particles it carries, obtains the projection measurement results containing the phase information of the quantum state to be prepared, and sends them to the receiver Bob; The receiver Bob performs corresponding unitary operations on the particles it carries according to the single-particle measurement result, the POVM measurement result and the projection measurement result to restore the quantum state to be prepared.

2. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 1, characterized in that: The direct entanglement channel is expressed as: Among them, the coefficients b0 and b1 are expressed as:

3. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 2, characterized in that: The joint system state of the intermediate node particle pair under the direct entanglement channel is expressed as:

4. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 2, characterized in that: The receiver Bob performs corresponding unitary operations on the particles he carries according to the format of the direct entanglement channel, including: When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=I=|0><0|+|1><1|; When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=X=|0><1|+|1><0|; When the direct entanglement channel is When the particle B of the receiver Bob q+1 Perform unitary operation U=Z=|0><0|-|1><1|; When the direct entanglement channel is When the particle B of the receiver Bob q+1 A unitary operation U=ZX=(|0><0|-|1><1|)(|0><1|+|1><0|) is performed.

5. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 1, characterized in that: After the first sender Alice1 performs a CNOT operation on its particle pair, it performs a single-particle measurement on the target quantum bit and a POVM measurement on the control quantum bit, and obtains a single-particle measurement result and a POVM measurement result containing the amplitude information of the quantum state to be prepared and sends them to the receiver Bob, including: The first sender Alice1 performs a CNOT operation on its particle pair (p1, A1) and performs a single-particle measurement on particle A1 with a basis of {|t>, t=0, 1}; The first sender Alice1 performs POVM measurement on particle p1, expressed as: in, The coefficient x satisfies 6. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 5, characterized in that: After the first sender Alice1 performs the CNOT operation on its particle pair (p1, A1), the joint system state of the intermediate node particle pair is expressed as: Among them, redefinition After that, the joint system state is expressed as:

7. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 1, characterized in that: The second sender Alice2 performs projection measurement on the particles it carries, obtains the projection measurement result containing the phase information of the quantum state to be prepared, and sends it to the receiver Bob, including: After the receiver Bob obtains the projection measurement result, he selects the preset phase measurement basis | n >(n=0,1) is:

8. The method for preparing quantum states based on bidirectional fault-tolerant multi-hop joint remote control according to claim 1, characterized in that: The receiver Bob performs corresponding unitary operations on the particles it carries according to the single-particle measurement result, the POVM measurement result and the projection measurement result to restore the quantum state to be prepared, including: The receiver Bob measures particle B based on the single particle measurement result. q+1 The first unitary operation performed is expressed as: The receiver Bob calculates the B after the first unitary operation based on the POVM measurement result and the projection measurement result. q+1 Perform the second unitary operation to restore the quantum state to be prepared include: If the POVM measurement result is |P0> and the projection measurement result is |O0>, then the second unitary operation is performed. If the POVM measurement result is |P0> and the projection measurement result is |O1>, the second unitary operation is performed. If the POVM measurement result is |P1> and the projection measurement result is |O0>, then the second unitary operation is performed. If the POVM measurement result is |P1> and the projection measurement result is |O1>, then the second unitary operation is performed If the POVM measurement result is |P2>, the preparation failure is returned.

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