Multi-party joint cluster state remote preparation method based on multicast

Abstract

The invention discloses a multiparty joint cluster state remote preparation method based on multicast. A sender, a plurality of joint preparation parties and a plurality of receivers are connected through a cluster state channel to establish a quantum entanglement channel; the amplitude value information and the phase value information of the to-be-prepared target state are respectively distributed between the sender and the plurality of joint preparation parties; performing measurement of an amplitude value measurement base on a particle held by a sender, and sending a result to a plurality of joint preparation parties and corresponding receivers; after receiving the amplitude measurement result sent by the sender, the joint preparation parties execute unitary operation and corresponding phase value measurement on the owned measurement basis, and send the phase measurement result to the next joint preparation party and the corresponding receiver until the last joint preparation party completes measurement; according to the measurement results of the sender and the plurality of joint preparation parties, the receiver performs unitary operation on the held particles to obtain a target intermediate state; and the receiver introduces auxiliary particles to execute CNOT and CZ operations to obtain a target cluster state.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum communication, and in particular to a remote preparation method for multi-party joint cluster states based on multicast. Background Art

[0002] As one of the key technologies in the field of quantum information processing, quantum remote state preparation aims to directly construct specific target quantum states at a long distance by using pre-shared entanglement resources. However, since it is difficult to achieve synchronous multi-party preparation in traditional state preparation schemes, quantum multicast communication has become an indispensable supporting technology because it can achieve various information transmission tasks with relatively low complexity and is widely used in fields such as quantum networks, quantum key distribution, and quantum computing. However, in an actual quantum communication network, the required states are interfered by factors such as noise in the environment, resulting in entanglement and a certain phase shift. In most of the proposed multicast state preparation schemes, the phase information of the target state is often completed by a single preparer during the preparation process, which will reduce the efficiency of the operator and there is also a possibility of losing the phase value. Finally, it affects the actual preparation result, resulting in inevitable errors and affecting the reliability of quantum communication. Summary of the Invention

[0003] Object of the Invention: In order to overcome the deficiencies in the prior art, the present invention provides a remote preparation method for multi-party joint cluster states based on multicast. By adding multiple joint preparers between the sender and multiple receivers and introducing auxiliary particles to multiple receivers, the preparation of quantum remote states is realized, and the success rate and accuracy of remote state preparation are improved.

[0004] Technical Solution: To achieve the above object, a remote preparation method for multi-party joint cluster states based on multicast of the present invention includes a sender Alice, multiple preparers r, and multiple receivers Bob; the method includes the following steps:

[0005] S1. Connect the sender Alice, multiple joint preparers R, and multiple receivers Bob through a cluster state channel to establish a quantum entanglement channel;

[0006] S2. Obtain the target state to be prepared, and distribute the amplitude value information and phase value information of the target state to be prepared between the sender Alice and multiple joint preparers R respectively;

[0007] S3. Perform a measurement of the amplitude value measurement basis on the particles held by the sender Alice, and send the amplitude measurement result to multiple joint preparers R and the corresponding receivers Bob through the channel;

[0008] S4. After each of the multiple joint preparers \(R\) receives the amplitude measurement result sent by the sender Alice, it performs the corresponding unitary operation and conducts the corresponding phase value measurement, and then sends the phase measurement result to the next joint preparer and the corresponding receiver Bob; until the last joint preparer completes the phase value measurement and sends the phase measurement result to the corresponding receiver Bob, the measurement process ends.

[0009] S5. After all measurements are completed, based on the measurement results of the sender Alice and the multiple joint preparers \(R\) obtained, the receiver Bob performs a unitary operation on the held particles to restore them to the initial target state form, obtaining the target intermediate state.

[0010] S6. The receiver Bob introduces auxiliary particles to perform the CNOT operation and the CZ operation to obtain the target cluster state.

[0011] Further, in the step S1, the multiple joint preparers \(R\) i \((i = 1, 2, \ldots, 2N - 2)\), and the multiple receivers Bob i \((i = 1, 2, \ldots, m)\); the sender Alice, the multiple joint preparers \(R\) and the multiple receivers Bob are connected through the cluster state channel, and the maximum entangled cluster state form is:

[0012]

[0013] The sender Alice holds the amplitude value information of the target state to be prepared and has qubits. The multiple joint preparers \(R\) i \((i = 1, 2, \ldots, 2N - 2)\) hold particles The particles held by the receiver Bob The sender Alice uses as the control particle, as the controlled particle, and performs the CZ operation; a quantum entanglement channel is established, and the initial state of the system is represented as:

[0014]

[0015] In the formula, \(m\) is the number of receivers, and \(N\) is the \(N\) in \(2N - 2\) which is the number of joint preparers.

[0016] Further, in the step S2, the sender Alice and the joint preparer \(R\) jointly prepare an arbitrary four - qubit cluster state for the receiver Bob. The four - qubit cluster state is the target state to be prepared, and the four - qubit cluster state is represented as follows:

[0017]

[0018] Wherein, α, β, μ, and v are the amplitude value information of the target state to be prepared, satisfying the normalization condition, is the phase value information of the target state to be prepared; the amplitude value information of the target state to be prepared is sent to the sender Alice, and the phase value information of the target state to be prepared is distributed among multiple joint preparers R i (i = 1, 2,..., 2N - 2), and the phase value information satisfies the following formula;

[0019]

[0020] Furthermore, in step S3, the amplitude value is measured according to the measurement basis form applied by the sender Alice on the particles, and the measurement basis form is as follows:

[0021]

[0022] Wherein, p i is the same as the amplitude value coefficient of the target state to be prepared;

[0023] After the sender Alice performs the measurement of the amplitude value measurement basis, the state of the amplitude measurement result of the 2m-bit particles is expressed as |r1r2…r m (r = 0, 1), and the decimal number X is used to represent all 2 2m kinds of amplitude measurement results in sequence, and the amplitude measurement results are synchronously sent to multiple joint preparers R and the corresponding receiver Bob.

[0024] Furthermore, in step S4, when the first joint preparer R1 receives the amplitude measurement result of the sender Alice, the first joint preparer R1 obtains the measurement basis form of the first joint preparer R1 according to the amplitude measurement result, and then the joint preparer R1 performs the measurement of part of the phase value to obtain the phase measurement result of the first joint preparer R1; the phase measurement result of the first joint preparer R1 and the amplitude measurement result of the sender Alice are sent to the second joint preparer R2 and the corresponding receiver Bob;

[0025] The second joint preparer R2 obtains its corresponding measurement basis form according to the amplitude measurement result, and then the joint preparer R2 performs the measurement of part of the phase value to obtain the phase measurement result of the second joint preparer R2; the phase measurement result of the second joint preparer R2 and the amplitude measurement result of the sender Alice are sent to the third joint preparer R3 and the corresponding receiver Bob;

[0026] And so on, until the last joint preparer R 2N-2 obtains its corresponding measurement basis form according to the amplitude measurement result, and then the joint preparer R 2N-2Measure partial phase values to obtain the last joint preparer R 2N-2 's phase measurement result; the last joint preparer R 2N-2 's phase measurement result is sent to the corresponding recipient Bob.

[0027] Furthermore, after each joint preparer R among multiple joint preparers obtains the form of the measurement basis, the joint preparer performs a measurement of partial phase values; the form of its measurement basis is as follows:

[0028]

[0029]

[0030] Multiple joint preparers R perform a 2m-bit quantum state phase value measurement, and the quantum states of all measured bits are represented in the following form There are a total of 2 2m phase measurement results represented by the decimal number y j (j = 2, 3,..., m).

[0031] Furthermore, the measurement basis and the unitary operation performed among the multiple joint preparers R both depend on the amplitude measurement result of the sender Alice's amplitude measurement. When the amplitude measurement result is α i |00> + β i |01> + μ i |10> + v i |11> (i = 1, 2,..., m), perform the unitary operation The phase value measurement basis is:

[0032]

[0033] When the amplitude measurement result is β i |00> - α i |01> + v i |10> - μ i |11> (i = 1, 2,..., m), perform the unitary operation The phase value measurement basis is:

[0034]

[0035] When the amplitude measurement result is μ i |00> - v i |1001> - α i |10> + β i |11> (i = 1, 2,..., m), perform the unitary operation The phase value measurement basis is:

[0036]

[0037] When the amplitude measurement result is v i |00> + μ i |01> - β i |10> - α i |11> (i = 1, 2,..., m), perform a unitary operation The phase value measurement basis is:

[0038]

[0039] Further, in step S5, multiple receivers Bob respectively perform unitary operations on the held particles to restore them to the initial target state form, obtaining a target intermediate state; the form of the unitary operation is as follows;

[0040]

[0041] After receiver Bob performs the unitary operation, an arbitrary two - qubit target intermediate state is obtained, and its form is as follows:

[0042]

[0043] Beneficial effects: A remote preparation method of a multi - party joint cluster state based on multicast according to the present invention realizes the preparation of a quantum remote state by adding multiple joint preparation parties between the sender and multiple receivers; separates the amplitude value information and phase value information of the target state and holds them by different nodes, optimizing the information distribution and processing process; combines the collaborative use of classical channels and quantum channels, improving the reliability and parallelism of the system; the modular operation process is convenient for expansion and maintenance; receiver Bob introduces auxiliary particles to perform CNOT and CZ operations to obtain the target cluster state, and the introduction and application of auxiliary particles further simplify the preparation process of the target cluster state, improving the success rate and accuracy. Description of the Drawings

[0044] Figure 1 is a flowchart of a remote preparation method of a multi - party joint cluster state based on multicast;

[0045] Figure 2 is a schematic diagram of particle distribution of a remote preparation method of a multi - party joint cluster state based on multicast;

[0046] Figure 3 is a schematic diagram of a quantum circuit of a remote preparation method of a multi - party joint cluster state based on multicast. Detailed Embodiment

[0047] The present invention will be further described in detail below with reference to the drawings.

[0048] As Figure 1As shown, a remote preparation method for a multi-party joint cluster state based on multicast includes a sender Alice, multiple preparers R, and multiple receivers Bob. By introducing multiple joint preparers, part of the information of the target state to be prepared is distributed to the multiple joint preparers. After each participating party performs the corresponding measurement operation, the measurement results are synchronously sent to the receiver and the unitary operation is performed. Then, auxiliary particles are introduced to perform the corresponding operations to obtain the target state to be prepared. The method includes the following steps:

[0049] S1. Connect the sender Alice, multiple joint preparers R, and multiple receivers Bob through a cluster state channel to establish a quantum entanglement channel.

[0050] S2. Obtain the target state to be prepared, and distribute the amplitude value information and phase value information of the target state to be prepared between the sender Alice and multiple joint preparers R respectively.

[0051] S3. Perform a measurement on the particles held by the sender Alice using the amplitude value measurement basis, and send the amplitude measurement result to multiple joint preparers R and the corresponding receivers Bob through the channel.

[0052] S4. After each joint preparer R in the multiple joint preparers R receives the amplitude measurement result sent by the sender Alice, perform the corresponding unitary operation on the possessed measurement basis to obtain the complete form of the measurement basis, which is the measurement basis form. And perform the corresponding phase value measurement, and send the phase measurement result to the next joint preparer and the corresponding receiver Bob. Until the last joint preparer completes the phase value measurement and sends the phase measurement result to the corresponding receiver Bob, the measurement process ends.

[0053] S5. After all measurements are completed, according to the measurement results of the sender Alice and multiple joint preparers R obtained, the receiver Bob performs a unitary operation on the held particles to restore to the initial target state form to obtain the target intermediate state.

[0054] S6. Based on the obtained target intermediate state, the receiver Bob introduces auxiliary particles to perform the CNOT operation and the CZ operation to obtain the target cluster state.

[0055] In the step S1, the multiple joint preparers R i (i = 1, 2,..., 2N - 2), and the multiple receivers Bob i (i = 1, 2,..., m); The sender Alice, multiple joint preparers R, and multiple receivers Bob are connected through a cluster state channel, and the form of the maximally entangled cluster state is:

[0056]

[0057] In the formula, Denotes the tensor product, which is used to combine the states of all qubits;

[0058] As Figure 2 shown, the sender Alice holds the qubits with the amplitude value information of the target state to be prepared. The particles held among the multiple joint preparers R i (i = 1, 2,..., 2N - 2).

[0059] The particles held by the receiver Bob For the entire state preparation process, in order to reduce the operation complexity of the preparation process, the sender Alice uses as the control particle, as the controlled particle, and performs the CZ operation; a quantum entanglement channel is established, and the initial state of the system is expressed as:

[0060]

[0061] In the formula, m is the number of receivers, and N is the N in 2N - 2, which is the number of joint preparers; Denotes the tensor product, which is used to combine the states of all qubits.

[0062] In step S2, the sender Alice and the joint preparer R jointly prepare an arbitrary four - qubit cluster state for the receiver Bob. The four - qubit cluster state is the target state to be prepared, and the four - qubit cluster state is expressed as follows:

[0063]

[0064] In the formula, α, β, μ, v are the amplitude value information of the target state to be prepared, satisfying the normalization condition, α 2 + β 2 + μ 2 + v 2 = 1; is the phase value information of the target state to be prepared; the amplitude value information and the phase value information of the target state to be prepared are distributed to the channel nodes among the sender Alice, the multiple joint preparers, and the receiver Bob; the amplitude value information of the target state to be prepared is sent to be held by the sender Alice, and the phase value information of the target state to be prepared is distributed to be held among the multiple joint preparers R i (i = 1, 2,..., 2N - 2), and the phase value information satisfies the following formula;

[0065]

[0066] The above formula means that the sum of the phases distributed by a finite number of preparers is the phase value information of the target state to be prepared.

[0067] In step S3, the amplitude value is measured according to the measurement basis form of the sender Alice acting on the particle. The measurement basis form of the amplitude value of the sender Alice is as follows:

[0068]

[0069]

[0070] where p i is the same as the amplitude value coefficient of the target state to be prepared; p i is the measurement information for the sender Alice to measure the amplitude value and is the measurement basis for the amplitude value; The matrix composed of... is the complete form of the measurement basis for amplitude measurement, that is, the measurement basis form for the amplitude value; |00…00> 2m ,..., |11…11> 2m all represent the state basis corresponding to the measurement basis or the particles in the sender Alice.

[0071] The sender Alice needs to perform m measurements on the 2m-bit quantum state. After the sender Alice performs the measurement of the amplitude measurement basis, the state of the amplitude measurement result of the 2m-bit particle is expressed as |r1r2…r m >(r = 0, 1), r is the binary numbers 0 and 1; and for the convenience of representation, the decimal number X is used to represent all 2 2m kinds of amplitude measurement results in turn, and the amplitude measurement results are sent synchronously to the first joint preparer R1 among multiple joint preparers R and the corresponding receiver Bob; mainly, the amplitude measurement results of the sender Alice are sent to all receivers Bob through the quantum entanglement channel.

[0072] In step S4, when the first joint preparer R1 receives the amplitude measurement result of the sender Alice, the first joint preparer R1 obtains the measurement basis of the first joint preparer R1 according to the amplitude measurement result, performs the corresponding unitary operation on the measurement basis obtained, and obtains the complete form of the measurement basis, that is, the measurement basis form; then the joint preparer R1 performs the measurement of the partial phase value to obtain the phase measurement result of the first joint preparer R1; the phase measurement result of the first joint preparer R1 and the amplitude measurement result of the sender Alice are sent to the second joint preparer R2 and the corresponding receiver Bob at the same time, that is, the receiver Bob1;

[0073] The second joint preparer R2 obtains its corresponding measurement basis according to the amplitude measurement result, performs the corresponding unitary operation on the possessed measurement basis to obtain the complete form of the measurement basis, which is the measurement basis form; then the joint preparer R2 measures a partial phase value to obtain the phase measurement result of the second joint preparer R2; the phase measurement result of the second joint preparer R2 and the amplitude measurement result of the sender Alice are sent to the third joint preparer R3 and the corresponding receiver Bob, which is the receiver Bob2 at the same time.

[0074] For any number of joint preparers to perform multi-particle measurement basis measurements on the particles at the nodes and send the measurement results to the joint preparers of the next adjacent node, and send the measurement results to the receivers at the same time.

[0075] And so on until the last joint preparer R 2N-2 Obtains its corresponding measurement basis according to the amplitude measurement result, performs the corresponding unitary operation on the possessed measurement basis to obtain the complete form of the measurement basis, which is the measurement basis form; then the joint preparer R 2N-2 Performs a partial phase value measurement to obtain the last joint preparer R 2N-2 's phase measurement result; the phase measurement result of the last joint preparer R 2N-2 Is sent to the corresponding receiver Bob, which is the receiver Bob m .

[0076] After each joint preparer of multiple joint preparers R obtains the measurement basis form, the joint preparer performs a partial phase value measurement; the phase value measurement basis form is as follows:

[0077]

[0078] In the formula, the measurement basis form is obtained according to the amplitude measurement result of the amplitude value measured by the sender Alice and the partial phase information. The composed matrix is the complete form of the phase measurement basis for performing the phase value measurement, which is the phase value measurement basis form. Is expressed as measurement information, which is the phase value measurement basis; |00…00> 2m ,..., |11…11|> 2m All represent the state bases corresponding to the measurement bases or the particles in the joint preparers. The joint preparer R performs a 2m-bit quantum state phase value measurement, and the quantum states of all measurement bits are represented in the following form It can be that the phase value measurement result of the 2m-bit quantum state is adopted Is expressed; a total of 2 2m Phase measurement results are represented by the decimal number y j (j = 2, 3,..., m).

[0079] The phase value information of each phase value measurement satisfies the constraint condition That is, after all phase measurements are completed, the phase vector sum form will be satisfied.

[0080] When the joint preparer R receives the measurement results of the sender Alice, it is necessary to perform the corresponding unitary operation on the measurement basis and complete the unitary operation before the phase value measurement; the unitary operations performed all depend on the amplitude measurement results of the sender Alice's amplitude measurement, and its unitary operations are as follows:

[0081]

[0082] In the formula, represents the measurement information For the specific unitary operation, corresponding unitary operations are performed according to the particle states of 0 and 1 in the amplitude measurement results.

[0083] When the first joint preparer R1 receives the amplitude measurement results of the sender Alice, the first joint preparer R1 obtains the measurement basis of the first joint preparer R1 according to the amplitude measurement results, performs the corresponding unitary operation on the owned measurement basis, and obtains the complete form of the measurement basis, which is the measurement basis form; then the joint preparer R1 performs partial phase value measurements, and an example of its measurement basis form is as follows:

[0084]

[0085] In all the joint preparers among the multiple joint preparers R, the measurement basis and the unitary operations performed on the measurement basis all depend on the amplitude measurement results of the sender Alice's amplitude measurement. When the amplitude measurement result is α i |00> + β i |01> + μ i |10> + v i |11> (i = 1, 2,..., m), the unitary operation is performed The phase value measurement basis is:

[0086]

[0087] When the amplitude measurement result is β i |00> - α i |01> + v i |10> - μ i |11> (i = 1, 2,..., m), the unitary operation is performed The phase value measurement basis is:

[0088]

[0089] When the amplitude measurement result is μi |00> - v i |1001> - α i |10> + β i When it is |11> (i = 1, 2,..., m), perform a unitary operation The phase value measurement basis is:

[0090]

[0091] When the amplitude measurement result is v i |00> + μ i |01> - β i |10> - α i When it is |11> (i = 1, 2,..., m), perform a unitary operation The phase value measurement basis is:

[0092]

[0093] The above four cases only show the measurement basis in the form of the phase value measurement basis under different conditions and the unitary operations performed; the complete form of the specific phase value measurement basis, that is, the measurement basis form still needs to be calculated through the measurement basis form formula.

[0094] In step S5, according to the amplitude measurement result of the sender Alice and the phase measurement results of multiple joint preparers R, multiple receivers Bob respectively perform unitary operations on the held particles to restore them to the initial target state form, obtaining a target intermediate state; the form of the unitary operation is as follows;

[0095]

[0096] In the formula, and are to perform corresponding unitary operations according to the 0 and 1 particle states of the measurement basis, which can be to perform corresponding unitary operations through the 0 and 1 particle states of the amplitude measurement result of the sender Alice and the phase measurement results of multiple joint preparers R.

[0097] After the receiver Bob performs the unitary operation, an arbitrary two - qubit target intermediate state is obtained, and its target intermediate state form is as follows:

[0098]

[0099] During the recovery operation, the matrix form of the unitary operation depends on the amplitude measurement results of the sender Alice and the results after measurement by each joint preparation party; it affects the bit flip of the final state for the sender Alice, while the joint preparation party causes the phase change of the final target state; for non-universal receivers, the form of the target state to be prepared depends on the results of their amplitude and phase value measurements; the matrix forms of the different unitary operations in the unitary operation are as follows, namely the Pauli matrices:

[0100]

[0101] ZX = (|0><0| - |1><1|)(|0><1| + |1><0|)

[0102] In the step S6, the receiver Bob introduces auxiliary particles to perform CNOT and CZ operations to obtain the target cluster state; multiple receivers Bob introduce m pairs of auxiliary particles respectively after obtaining any two-qubit state, so as to further realize the preparation of the target cluster state; the auxiliary particles are as follows:

[0103]

[0104] Each receiver uses the particle as the control particle and sequentially performs the CNOT operation on the particle ; meanwhile is the control particle, is the controlled particle, and performs the CZ operation; finally, the quantum state representation of the arbitrary four-qubit cluster state to be prepared is:

[0105]

[0106] The CNOT operation is a controlled-NOT gate, which 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 flips from |0> to |1>, or from |1> to |0>. The matrix form corresponding to the CNOT operation is:

[0107]

[0108] The CZ operation, Controlled-Z Gate, is an important two-qubit logic gate. Its core function is to realize the phase flip of the quantum state by controlling the interaction between the control qubit and the target qubit, thereby providing basic support for key technologies such as quantum entanglement generation, quantum key distribution, and quantum teleportation; the matrix form corresponding to the CZ operation is:

[0109]

[0110] Example

[0111] Based on one sender Alice, two intermediate joint preparation parties R1, R2, and two receivers Bob, the above-mentioned remote preparation method of multi-party joint cluster state based on multicast is realized; the method includes the following steps:

[0112] The sender Alice, multiple joint preparation parties R, and multiple receivers Bob are connected through a cluster state channel to establish a quantum entanglement channel. The form of the maximum entanglement cluster state is:

[0113]

[0114] The sender Alice holds the amplitude value information of the target state to be prepared and has quantum bits There are particles between the joint preparation parties R1 and R2 The particles held by the receivers Bob1 and Bob2 For the entire state preparation process, in order to reduce the operation complexity of the preparation process, the sender Alice uses as the control particle, as the controlled particle, and performs the CZ operation; a quantum entanglement channel is established, and the initial state of the system is expressed as:

[0115]

[0116] The sender Alice and the joint preparation party R jointly prepare an arbitrary four-qubit cluster state for the receiver Bob. The four-qubit cluster state is the target state to be prepared, and the four-qubit cluster state is expressed as follows:

[0117]

[0118] In the formula, α, β, μ, v are the amplitude value information of the target state to be prepared, satisfying the normalization condition, α 2 +β 2 +μ 2 +v 2 = 1; is the phase value information of the target state to be prepared; the amplitude value information and phase value information of the target state to be prepared are distributed to the channel nodes between the sender Alice, multiple joint preparation parties, and the receiver Bob; the amplitude value information of the target state to be prepared is sent to be held by the sender Alice, and the phase value information of the target state to be prepared is distributed to be held between the multiple joint preparation parties R1 and R2, and the phase value information satisfies the following formula;

[0119]

[0120] Measure the amplitude value according to the measurement basis form applied by the sender Alice on the particle, and the measurement basis form is as follows:

[0121]

[0122] where p i is the same as the amplitude value coefficient of the target state to be prepared; p i is the measurement basis form applied by the sender Alice on the particle. The sender Alice needs to perform 2 measurements of two-bit quantum states;

[0123] After the sender Alice performs the measurement of the amplitude value measurement basis, represent the state of the amplitude measurement result of the 4-bit particle as |r1r2…r m >(r = 0, 1), r is the binary numbers 0 and 1; and for convenience of representation, use the decimal number X to represent all 16 amplitude measurement results in sequence, and synchronously send the amplitude measurement results to the joint preparer R1 and the corresponding receivers Bob1 and Bob2 among multiple joint preparers.

[0124] When the joint preparer R1 receives the amplitude measurement result of the sender Alice, the joint preparer R1 obtains the measurement basis form of the joint preparer R1 according to the amplitude measurement result, and performs the corresponding unitary operation. Then, the joint preparer R1 performs the measurement of the partial phase value, and the measurement basis form is as follows:

[0125]

[0126] There are 16 possible specific unitary operations here, and their forms depend on the form of Alice's amplitude measurement result. The relationship between the unitary operation of the measurement basis corresponding to the joint preparer and Alice's measurement result is shown in Table 1 specifically:

[0127] R1

[0128] Table 1 Relationship table between the unitary operation of the measurement basis corresponding to the joint preparer R1 and Alice's measurement result

[0129]

[0130] The measurement basis of the joint preparer R1 is as follows, and the complete form of the phase measurement basis is calculated through the formula, which is the measurement basis form;

[0131]

[0132] After the joint preparer R1 completes the phase value measurement operation, the phase measurement result and is represented by the decimal y1; the phase measurement result of the joint preparation party R1 and the amplitude measurement result of the sender Alice are synchronously sent to the next joint preparation party r2 and the receiver Bob1 through a classical channel.

[0133] After receiving the phase measurement result of the joint preparation party R1 and the amplitude measurement result of the sender Alice, the joint preparation party R2 first performs a unitary operation, and its matrix form copies the measurement result. The relationship between the unitary operation of the measurement basis corresponding to the joint preparation party R2 and the measurement result of Alice is shown in Table 2 below:

[0134] Table 2 Relationship between the unitary operation of the measurement basis corresponding to the joint preparation party R2 and the measurement result of Alice

[0135]

[0136] For the two joint preparation parties to perform multi-particle measurement basis measurements on the particles at the node, and send the measurement results to the joint preparation party of the next adjacent node, and at the same time send the measurement results to the receiver; after the last joint preparation party completes the measurement, the phase value measurement result of the joint preparation party R2 is sent to the receiver Bob2, and the measurement process ends.

[0137] After all measurements are completed, the receivers Bob1 and Bob2 perform unitary operations on the particles they hold according to the measurement results of the sender Alice and multiple joint preparation parties, and restore them to the initial target state form to obtain the target intermediate state; here, two joint preparation parties prepare the target states of the two receivers, and a total of three participants perform 6-bit particle state measurements. Since the measurement results have been given in binary form before, the form of the unitary operation that each receiver needs to perform is a total of 2 6 kinds; for the case of two receivers, in order to obtain the two-bit state in the above form, combined with the previous measurement results, the form of the unitary operation is:

[0138]

[0139] After performing the unitary operation, the target intermediate state is obtained:

[0140]

[0141] The receiver Bob introduces auxiliary particles to perform CNOT and CZ operations to obtain the target cluster state; multiple receivers Bob introduce 2 pairs of auxiliary particles respectively after obtaining any two-bit state in order to further realize the preparation of the target cluster state; the auxiliary particles are as follows:

[0142]

[0143] Each receiver Bob will use the particle As control particles, the particles are successively subjected to CNOT operations; meanwhile is the control particle, is the controlled particle, and the CZ operation is performed; finally, the quantum state representation of any four-qubit cluster state to be prepared is obtained as:

[0144]

[0145] Here, the receiver obtains the quantum state of any four-qubit cluster state to be prepared, completing the remote preparation of the multi-party joint cluster state based on multicast; as Figure 3 shown, it is a schematic diagram of the quantum circuit of the remote preparation method of the multi-party joint cluster state based on multicast.

[0146] The above is only a description of the preferred embodiments of the present invention. Those of ordinary skill in the art can make several modifications and optimizations based on the above disclosure without departing from the basic principle content. These improvements and optimizations should be regarded as the protection scope understood by the present invention.

Claims

1. A remote preparation method for multi-party joint cluster states based on multicast, characterized in that: It includes a sender Alice, multiple preparation parties R, and multiple receivers Bob; the following steps are included: S1. Connect the sender Alice, multiple joint preparation parties R, and multiple receivers Bob through a cluster state channel to establish a quantum entanglement channel; S2. Obtain the target state to be prepared, and distribute the amplitude value information and phase value information of the target state to be prepared between the sender Alice and multiple joint preparation parties R respectively; S3. Perform a measurement on the particles held by the sender Alice using the amplitude value measurement basis, and send the amplitude measurement result through the channel to multiple joint preparation parties R and the corresponding receivers Bob; S4. After each joint preparation party R in the multiple joint preparation parties R receives the amplitude measurement result sent by the sender Alice, perform the corresponding unitary operation and conduct the corresponding phase value measurement, and send the phase measurement result to the next joint preparation party and the corresponding receiver Bob; until the last joint preparation party completes the phase value measurement and sends the phase measurement result to the corresponding receiver Bob, the measurement process ends; S5. After all measurements are completed, according to the measurement results of the sender Alice and multiple joint preparation parties R obtained, the receiver Bob performs a unitary operation on the held particles to restore them to the initial target state form, obtaining the target intermediate state; S6. The receiver Bob introduces auxiliary particles to perform the CNOT operation and the CZ operation to obtain the target cluster state.

2. The remote preparation method of a multi-party joint cluster state based on multicast according to claim 1, characterized in that: In the step S1, multiple joint preparers R i (i = 1, 2,..., 2N - 2), multiple receivers Bob i (i = 1, 2,..., m); the sender Alice, multiple joint preparers R, and multiple receivers Bob are connected through a cluster state channel, and the maximum entangled cluster state form is: The sender Alice holds quantum bits with the amplitude value information of the target state to be prepared. The multiple joint preparers R i (i = 1, 2,..., 2N - 2) hold particles The particles held by the recipient Bob The sender Alice uses as the control particles as the controlled particles and performs the CZ operation; establish a quantum entanglement channel, that is, the initial state of the system is expressed as: In the formula, m is the number of receivers, and N is the N in 2N - 2 which is the number of joint preparation parties.

3. The remote preparation method of a multi-party joint cluster state based on multicast according to claim 2, characterized in that: In the step S2, the sender Alice and the joint preparation party R jointly prepare an arbitrary four-qubit cluster state for the receiver Bob. The four-qubit cluster state is the target state to be prepared, and the four-qubit cluster state is expressed as follows: where α, β, μ, and ν are the amplitude value information of the target state to be prepared, satisfying the normalization condition, α 2 + β 2 + μ 2 + ν 2 = 1; is the phase value information of the target state to be prepared; the amplitude value information of the target state to be prepared is sent to the sender Alice, and the phase value information of the target state to be prepared is distributed among multiple joint preparers R i (i = 1, 2,..., 2N - 2), and the phase value information satisfies the following formula; 4. A remote preparation method of a multi-party joint cluster state based on multicast according to claim 1, characterized in that: In the step S3, the amplitude value is measured according to the measurement basis form applied by the sender Alice on the particles, and its measurement basis form is as follows: where p i is the same as the amplitude value coefficient of the target state to be prepared; After the sender Alice performs the measurement of the amplitude value measurement basis, the state of the amplitude measurement result of the 2m-bit particle is expressed as |r1r2...r m >(r = 0, 1), and the decimal number X is used to represent all 2 2m kinds of amplitude measurement results in turn, and the amplitude measurement results are synchronously sent to multiple joint preparation parties R and the corresponding receivers Bob.

5. A remote preparation method of a multi-party joint cluster state based on multicast according to claim 1, characterized in that: In the step S4, when the first joint preparation party R1 receives the amplitude measurement result of the sender Alice, the first joint preparation party R1 obtains the measurement basis form of the first joint preparation party R1 according to the amplitude measurement result, and then the joint preparation party R1 conducts a partial phase value measurement to obtain the phase measurement result of the first joint preparation party R1; the phase measurement result of the first joint preparation party R1 and the amplitude measurement result of the sender Alice are sent to the second joint preparation party R2 and the corresponding receiver Bob; The second joint preparation party R2 obtains its corresponding measurement basis form according to the amplitude measurement result, and then the joint preparation party R2 conducts a partial phase value measurement to obtain the phase measurement result of the second joint preparation party R2; the phase measurement result of the second joint preparation party R2 and the amplitude measurement result of the sender Alice are sent to the third joint preparation party R3 and the corresponding receiver Bob; And so on until the last joint preparer R 2N-2 Obtain the corresponding measurement basis form according to the amplitude measurement result, and then the joint preparer R 2N-2 Measure some phase values to obtain the phase measurement result of the last joint preparer R 2N-2 ; The phase measurement result of the last joint preparer R 2N-2 Send the phase measurement result to the corresponding recipient Bob.

6. The remote preparation method of a multi-party joint cluster state based on multicast according to claim 2, characterized in that: After each joint preparation party R in the multiple joint preparation parties R obtains the measurement basis form, the joint preparation party conducts a partial phase value measurement; its measurement basis form is as follows: Multiple joint preparation methods R are used to measure the phase values of 2m-bit quantum states, and the quantum states of all measured bits are represented in the following form A total of 2 2m phase measurement results are represented by the decimal number y j (j = 2, 3,..., m).

7. A remote preparation method of a multi-party joint cluster state based on multicast according to claim 6, characterized in that: In the multiple joint preparation methods R, both the measurement bases and the implemented unitary operations depend on the amplitude measurement result of the amplitude value measured by the sender Alice. When the amplitude measurement result is α i |00> + β i |01> + μ i |10> + v i |11> (i = 1, 2,..., m), the unitary operation is performed The phase value measurement basis is: When the amplitude measurement result is β i |00> - α i |01> + v i |10> - μ i |11> (i = 1, 2,..., m), perform a unitary operation The phase value measurement basis is: When the amplitude measurement result is μ i |00> - v i |1001> - α i |10> + β i |11> (i = 1, 2,..., m), perform the unitary operation The phase value measurement basis is: When the amplitude measurement result is v i |00> + μ i |01> - β i |10> - α i |11> (i = 1, 2,..., m), perform a unitary operation The phase value measurement basis is:

8. A remote preparation method of a multi-party joint cluster state based on multicast according to claim 1, characterized in that: In the step S5, multiple receivers Bob respectively perform unitary operations on the held particles to restore them to the initial target state form, obtaining target intermediate states; the form of the unitary operation is as follows: After the receiver Bob performs the unitary operation, an arbitrary two-bit target intermediate state is obtained, and its form is as follows:

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