The setup and working method of multi-particle state teleportation based on different energy level channels

Abstract

The present invention discloses the setting and working method of invisible transmission of multi-particle states based on channels with different energy levels, including the following steps: Step 1: determine system transmission, including the dimension and number of transmitted particles, and the dimension and number of channel entangled pairs; Step 2: the sender performs a controlled modular addition unitary transformation on the transmitted multi-particle state and the channel part; Step 3: the sender sends the measurement result to the receiver Bob through a traditional channel, and the measurement result includes first performing Fourier transformation on the mixed state respectively; Step 4: the receiver performs a recovery operation on the particles of the shared channel according to the transmitted information; Step 5: the receiver uses an auxiliary particle to perform a unitary operation, and after measuring the particles of the channel part, performs a corresponding recovery matrix to obtain the original mixed entangled state. The present invention can use the existing entangled pairs of different energy levels for transmission, thereby improving the effectiveness of information transmission in the process of quantum communication.

Description

Technical Field

[0001] The present invention relates to the technical field of communication networks, and in particular to a setting and working method for invisible transmission of multi-particle states based on channels with different energy levels. Background Art

[0002] Quantum teleportation has attracted widespread attention since it was proposed. By utilizing the entangled pairs shared by the communicating parties, the sender can transmit its own state to the other side far away instead of directly transmitting particles. At present, quantum teleportation has made great progress both in theory and experiment. In 1997, quantum teleportation was demonstrated in experiments. If the entanglement quality of particles deteriorates due to decoherence when they are stored or transmitted in a noisy channel, entanglement purification is needed to improve the entanglement quality. In addition, the previous experiment was improved by using trapped calcium ions to perform deterministic quantum state teleportation between entangled pairs. After the protocol was determined, subsequent research was mainly divided into two directions: combating decoherence noise and high-dimensional or multi-particle teleportation. One of the representative experiments showed the non-locality based on high-fidelity six-photon GHZ states.

[0003] In recent years, several experiments on high-dimensional teleportation have been developed and are gaining increasing attention. These schemes demonstrate high reliability of entanglement in high-dimensional space generated in optical devices. For multi-particle teleportation, the properties of multi-qubits are a hot research topic, and their scope can be extended to a wider range of applications through various protocols. In addition, several proposed protocols that can be used in complex quantum networks demonstrate the main building blocks of future quantum networks and open the door to explore multi-node protocols and applications based on remote transmission. In addition, quantum parallel teleportation of multiple quantum states through different paths was proposed in 2021, which proved that this method has good performance in terms of communication cost and latency, where the unknown states of multi-qubits of mixed dimensions can be remotely transmitted through quantum channels of different dimensions. Summary of the invention

[0004] The purpose of the present invention is to provide a setting and working method for invisible transmission of multi-particle states based on channels with different energy levels, so as to solve the problems in the prior art.

[0005] To achieve the above object, the present invention provides the following technical solution: a setting and working method for multi-particle state invisible transmission based on different energy level channels, comprising the following steps:

[0006] Step 1: Determine the system transmission, including the dimension and number of transmitted particles, and the dimension and number of channel entangled pairs;

[0007] Step 2: The sender performs a controlled modular addition unitary transformation on the transmitted multi-particle state and the channel part;

[0008] Step 3: The sender sends the measurement results to the receiver Bob through the traditional channel. The measurement results include first performing Fourier transform on the mixed state respectively;

[0009] Step 4: The receiver performs recovery operations on some particles in the shared channel according to the transmitted information;

[0010] Step 5: The receiver uses auxiliary particles to perform unitary operations, and after measuring some particles in the channel, it makes a corresponding recovery matrix to obtain the original mixed entangled state.

[0011] Preferably, step 1: determine the parameters for hybrid teleportation between the sender Alice and the target receiver Bob, including the hybrid dimensional state to be prepared and transmitted: The coefficient is a superposition state |d1d2...d k >corresponding amplitude, and satisfying The number L of H-dimensional entangled pairs shared by Alice and Bob is determined by the specific transmission of particle states, and can be written in direct product multiplication form and simplified as follows:

[0012]

[0013] The state |n> represents the superposition state formed by L H-dimensional particles, such as |1> represents |00...1>, and the numbers in brackets correspond to the measurement results of each particle. The subscripts A and B represent their respective owners Alice and Bob.

[0014] Preferably, the step 2: treating the two parts mentioned in step 1 as a whole system |ψ>0

[0015]

[0016] where α i is the amplitude corresponding to system state i, is the normalization coefficient of the whole system. Afterwards, according to the serial number i, the control module addition operation of the mixed entangled state is performed with the multi-dimensional mixed state particle state as the control party and the shared state as the target. Each channel shared particle state is module added with the label of the corresponding control state:

[0017]

[0018] in Represents state n+i modulo H L addition.

[0019] Preferably, in step 3: in order to transmit the amplitude and phase information of the mixed superposition state through the channel, it is necessary to perform quantum Fourier transform of corresponding dimensions on the K particles of the mixed state to be transmitted respectively; the remaining channel entangled pair of the entire system includes the phase information of the original multi-particle state and the controlled bit migration generated by the controlled unitary operation; after K Fourier transforms, the system becomes:

[0020]

[0021] For a D-dimensional particle, the corresponding Fourier transform is:

[0022]

[0023] in is the normalization coefficient of the matrix, satisfying Unitary condition. Then the mixed particle state is measured separately and K measurement results are obtained |d K d K-1 ...d1>, the whole system becomes:

[0024]

[0025] where i k is the kth bit of the sequence number i, d k are the kth measurement results, and they together constitute the phase coefficients.

[0026] Preferably, in step 4, Alice performs standard basis measurement on the shared particle pairs she has, and according to the measurement result |m L m L-1 ...m1> A The L H-dimensional particles owned by Bob are transformed into the form determined by the measurement results on both sides and written as where β i for In order to restore the form of expressing K mixed-dimensional particle states with L H dimensions, Bob needs to perform three different unitary operations corresponding to the measurement results. and Transform to restore.

[0027]

[0028]

[0029]

[0030] exist In the back to h LThe coefficient of the term can be any complex number u modulo 1 i .

[0031] After applying the three matrices in sequence, the remaining system becomes:

[0032]

[0033] The above is transformed into a form of using H-dimensional particles to express mixed particle states of different dimensions. h L h L-1 ...h1>corresponding coefficient.

[0034] Preferably, in step 5, in order to transform the multi-particle state obtained in the previous step to its original form, the receiver Bob needs to continue to perform controlled unitary operations on the restored multi-particle state and then measure it. K initial particles corresponding to the original multi-particle state need to be prepared as auxiliary particles. The system for the receiver to perform controlled unitary operations is written as:

[0035]

[0036] Imitate the previous construction of the controlled unitary and execute it on its L+K particles:

[0037]

[0038] And after Fourier transforming the L channel particles respectively, we get (the specific form of Fourier transform will be given in the next section):

[0039]

[0040] in The measurement result is |m L m L-1 ...m1> causes the phase influence on each superposition state. Therefore, after obtaining the new L results |m L m L-1 ...m1>, the remaining K mixed-dimensional particle states become:

[0041]

[0042] Finally, the original K mixed entangled states are restored through the measurement results. In order to eliminate the phase effect, we perform a diagonal operation U4 on the remaining K particles:

[0043]

[0044]

[0045] where i lrepresents the lth particle in state i, m l is the result of the lth measured particle in the shared channel. Finally, the mixed entangled state to be transferred is obtained.

[0046] Preferably, the total number of states included in the transmission channel is greater than the total number of states included in the multi-particles that need to be transmitted, and the restriction conditions are such that resources are effectively utilized.

[0047] Preferably, a corresponding control modular addition operation is performed according to the serial number of each superposition state; and the conversion and recovery of dimensions between multi-particle states are achieved by utilizing unitary operations acting on particles of different dimensions.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. The present invention is based on the transmission of shared pairs between existing nodes and can be extended to any situation according to existing parameters. Therefore, the present invention improves the efficiency of information transmission.

[0050] 2. The non-local controlled operation adopted in the present invention is unitary, the measurements adopted in the invention are all single-particle measurements, and both classical communication and local operation are feasible.

[0051] 3. The present invention uses GHZ channels and Bell chain channels. Even if the remote nodes do not directly share quantum entangled pairs, quantum state information can still be transmitted between the two parties, which can meet the requirements of building a complex quantum communication network. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0053] Figure 1 It is a circuit schematic diagram of the present invention;

[0054] Figure 2 is a flow chart of the present invention;

[0055] Figure 3 It is a schematic diagram of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 ordinary technicians in this field without making creative work belong to the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0057] Description of technical terms of the present invention:

[0058] 1. Arbitrary mixed-dimensional multi-particle target state:

[0059] The form of any multi-bit target state for teleportation of the present invention is as follows:

[0060]

[0061] Where D K Represents different dimensions in the mixed state, For each corresponding entangled state |d1d2...d k >The amplitude of. Satisfy the normalization condition

[0062] 2. H measurement

[0063] H measurement is to first let the particle to be measured pass through a Hadamard gate, and then measure the particle to be measured on the |0>,|1> basis.

[0064] 3. Pauli's team:

[0065]

[0066]

[0067]

[0068]

[0069] 4. D-dimensional Fourier transform

[0070] For a D-dimensional state, the Fourier transform transforms its action It can be written in matrix form:

[0071]

[0072] It is easy to verify that the transformation satisfies the unitary condition and satisfies the H measurement case when D=2.

[0073] 5. Modular addition operation

[0074] For a map modulo d plus n It is easy to find that the inverse mapping is a modular subtraction mapping. The modular addition n can be regarded as a generalization of the Pauli matrix X in high dimensions:

[0075]

[0076] Embodiment 1

[0077] See also Figure 1-3 In an embodiment of the present invention, the setting and working method of multi-particle state invisible transmission based on different energy level channels includes the following steps:

[0078] Step 1: Determine the system transmission, including the dimension and number of transmitted particles, and the dimension and number of channel entangled pairs;

[0079] Step 2: The sender performs a controlled modular addition unitary transformation on the transmitted multi-particle state and the channel part;

[0080] Step 3: The sender sends the measurement results to the receiver Bob through the traditional channel. The measurement results include first performing Fourier transform on the mixed state respectively;

[0081] Step 4: The receiver performs recovery operations on some particles in the shared channel according to the transmitted information;

[0082] Step 5: The receiver uses auxiliary particles to perform unitary operations, and after measuring some particles in the channel, it makes a corresponding recovery matrix to obtain the original mixed entangled state.

[0083] Preferably, step 1: determine the parameters for hybrid teleportation between the sender Alice and the target receiver Bob, including the hybrid dimensional state to be prepared and transmitted: The number L of H-dimensional entangled pairs shared by Alice and Bob is determined by the specific transmission of particle states, and can be written in direct product multiplication form and simplified as follows:

[0084]

[0085] Preferably, the step 2: treating the two parts mentioned in step 1 as a whole system |ψ>0

[0086]

[0087] According to the serial number, the multi-dimensional mixed state particle state is used as the control party and the shared state is used as the target to perform the control modular addition operation on the mixed entangled state; each channel shared particle state is modularly added with the label of the corresponding control state:

[0088]

[0089] Preferably, in step 3: in order to transmit the amplitude and phase information of the mixed superposition state through the channel, it is necessary to perform quantum Fourier transform of corresponding dimensions on the K particles of the mixed state to be transmitted respectively; the remaining channel entangled pair of the entire system includes the phase information of the original multi-particle state and the controlled bit migration generated by the controlled unitary operation; after K Fourier transforms, the system becomes:

[0090]

[0091] Then the mixed particle state is measured separately and K measurement results are obtained |d K d K-1 ...d1>, the whole system becomes:

[0092]

[0093] Preferably, in step 4, Alice performs standard basis measurement on the shared particle pairs she has, and according to the measurement result |m L m L-1 ...m1> A The L H-dimensional particles owned by Bob are transformed into the form determined by the measurement results on both sides and written as In order to restore the form of expressing K mixed-dimensional particle states with L H dimensions, Bob needs to perform three different unitary operations corresponding to the measurement results. and Transform to restore; finally the result becomes:

[0094]

[0095] As above, H-dimensional particles are used to express the form of mixed particle states of different dimensions.

[0096] Preferably, in step 5: in order to transform the multi-particle state obtained in the previous step to the original form; the receiver Bob needs to continue to perform controlled unitary operation on the restored multi-particle state and then measure it; it is necessary to prepare K initial particles corresponding to the original multi-particle state as auxiliary particles for preparation; the system for the controlled unitary operation of the receiver is written as:

[0097]

[0098] Following the previous construction of the controlled unitary, execute the following on its L+K particle machine:

[0099]

[0100] And after Fourier transforming the L channel particles respectively, we get:

[0101]

[0102] Then measure it and get new L results |m L m L-1 ...m1> makes the K mixed particle states become:

[0103]

[0104] Finally, the original K mixed entangled states are restored through the measurement results.

[0105]

[0106] Preferably, the total number of states included in the transmission channel is greater than the total number of states included in the multi-particles that need to be transmitted, and the restriction conditions are such that resources are effectively utilized.

[0107] Preferably, a corresponding control modular addition operation is performed according to the serial number of each superposition state; and the conversion and recovery of dimensions between multi-particle states are achieved by utilizing unitary operations acting on particles of different dimensions.

[0108] Example 2: Transmitting 3D particles through a 2D entangled channel, specific steps:

[0109] Step 1: Determine the parameters for hybrid dimensional teleportation between sender Alice and target receiver Bob. Under the premise of satisfying redundancy and effectiveness, it can be determined that two 2D entangled pairs are required for the transmission of 3D qudits. The hybrid dimensional state to be transmitted is: The channel composed of two 2D entangled pairs can be written as:

[0110]

[0111] Step 2: Write the entire system in direct product form and simplify it as follows, treating the two parts mentioned in the previous step as a whole system |ψ>0:

[0112]

[0113] According to the serial number, the multi-dimensional mixed state particle state is used as the control party and the shared state is used as the target to perform the control modular addition operation of the mixed entangled state. Each channel shared particle state is modularly added with the label of the corresponding control state:

[0114]

[0115] According to the previous definition, the controlled unitary operation can be written as:

[0116]

[0117] For the sub-block matrices, there is a form of modular addition i. For the four modular addition matrices, there are:

[0118]

[0119]

[0120] Step 3: In order to transmit the amplitude and phase information of the mixed superposition state through the channel, it is necessary to perform quantum Fourier transforms of the corresponding dimensions on the two particles of the mixed state to be transmitted. The entire system is left with a channel entangled pair containing the phase information of the original multi-particle state and the controlled bit migration generated by the controlled unitary operation. After two Fourier transforms, the system becomes:

[0121]

[0122] For a 3D particle, the corresponding Fourier transform is:

[0123]

[0124] After that, the 3D qudit to be transferred is measured and the measurement result |d1> is obtained. The whole system becomes:

[0125]

[0126] Step 4: Alice performs standard basis measurement on the shared particle pair she owns. Based on the measurement result |m> A The two 2D particles that Bob has are transformed into the form determined by the measurement results on both sides and written as In order to restore the form of expressing K mixed-dimensional particle states with L H dimensions, Bob needs to perform three different unitary operations corresponding to the measurement results. and Transform to restore. Corresponding to the previous 4 types of modular addition matrices

[0127]

[0128]

[0129] Finally, the result becomes:

[0130]

[0131] The above is a form of using 2D channel particles to express mixed particle states of different dimensions.

[0132] Step 5: In order to transform the multi-particle state obtained in the previous step to its original form, the receiver Bob needs to continue to perform controlled unitary operations on the restored multi-particle state and then measure it. K initial particles corresponding to the original multi-particle state need to be prepared as auxiliary particles. The system for the receiver to perform controlled unitary operations is written as:

[0133]

[0134] Imitate the previous construction of the controlled unitary and execute it on its 1+2 particles:

[0135]

[0136] The unitary operation is

[0137]

[0138] Each block matrix still corresponds to the modular addition transformation matrix of control i. After Fourier transforming the two channel particles respectively, we get:

[0139]

[0140] Then measure it to get new L results |m2m1> so that the 3D qudit becomes:

[0141]

[0142] Finally, the original two mixed entangled states are restored through measurement results.

[0143]

[0144]

[0145] Example 3: Transmitting 2D-3D mixed state particles through a 4D entangled channel, specific steps:

[0146] Step 1: Determine the parameters for hybrid teleportation between sender Alice and target receiver Bob. Under the premise of satisfying redundancy and effectiveness, it can be determined that two 4-dimensional entangled pairs are required for hybrid state transmission. The hybrid dimensional state to be transmitted is: The entire system can be written in direct product form and simplified as follows:

[0147]

[0148] Step 2: Consider the two parts mentioned in the previous step as a whole system |ψ>0

[0149]

[0150] According to the serial number, the multi-dimensional mixed state particle state is used as the control party and the shared state is used as the target to perform the control modular addition operation of the mixed entangled state. Each channel shared particle state is modularly added with the label of the corresponding control state:

[0151]

[0152] According to the previous definition, the controlled unitary operation can be written as:

[0153]

[0154] For the sub-block matrices, there is a form of modular addition i:

[0155]

[0156] Step 3: In order to transmit the amplitude and phase information of the mixed superposition state through the channel, it is necessary to perform quantum Fourier transforms of the corresponding dimensions on the two particles of the mixed state to be transmitted. The entire system is left with a channel entangled pair containing the phase information of the original multi-particle state and the controlled bit migration generated by the controlled unitary operation. After two Fourier transforms, the system becomes:

[0157]

[0158] For a 3D particle, the corresponding Fourier transform is:

[0159]

[0160] For a 2D particle, the corresponding Fourier transform degenerates into Hadmard transform. Then the mixed particle state is measured and two measurement results |d2d1> are obtained. The whole system becomes:

[0161]

[0162] Step 4: Alice performs standard basis measurement on the shared particle pair she owns. Based on the measurement result |m2m1> A The L H-dimensional particles owned by Bob are transformed into the form determined by the measurement results on both sides and written as In order to restore the form of expressing K mixed-dimensional particle states with L H dimensions, Bob needs to perform three different unitary operations corresponding to the measurement results. and Transform to restore.

[0163]

[0164]

[0165]

[0166] Finally, the result becomes:

[0167]

[0168] The above is a form of using 4-dimensional particles to express mixed particle states of different dimensions.

[0169] Step 5: In order to transform the multi-particle state obtained in the previous step to its original form, the receiver Bob needs to continue to perform controlled unitary operations on the restored multi-particle state and then measure it. K initial particles corresponding to the original multi-particle state need to be prepared as auxiliary particles. The system for the receiver to perform controlled unitary operations is written as:

[0170]

[0171] Imitate the previous construction of controlled unitary and execute it on its 2+2 particles:

[0172]

[0173] The unitary operation is

[0174]

[0175] Each block matrix is ​​the modulo-addition transformation matrix corresponding to control i:

[0176]

[0177] After Fourier transforming the two channel particles respectively, we get:

[0178]

[0179] Then we measure it and get L new results |m2m1>, which makes the K mixed particle states become:

[0180]

[0181] Finally, the original two mixed entangled states are restored through measurement results.

[0182]

[0183]

[0184] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. The setting and working method of multi-particle state teleportation based on different energy level channels is characterized by: The following steps are involved: Step 1: Determine the system transmission, including the dimension and number of transmitted particles, and the dimension and number of channel entangled pairs; Step 2: The sender performs a controlled modular addition unitary transformation on the transmitted multi-particle state and the channel part; Step 3: The sender sends the measurement results to the receiver Bob through the traditional channel. The measurement results include first performing Fourier transform on the mixed state respectively; Step 4: The receiver performs recovery operations on some particles in the shared channel according to the transmitted information; Step 5: The receiver uses the auxiliary particle to perform unitary operation, and after measuring some particles in the channel, it makes the corresponding recovery matrix to obtain the original mixed entangled state; Step 1: Determine the parameters for hybrid teleportation between the sender Ali ce and the target receiver Bob, including the hybrid dimensional state to be prepared: Where D k are the dimensions of the k particles to be transferred, For each superposition state, the amplitude corresponds to The number L of H-dimensional entangled pairs shared by Ali ce and Bob is determined by the specific transmission of particle states, and it can be written in direct product multiplication form and simplified as follows: where α i is the amplitude corresponding to system state i, is the normalization coefficient of the whole system; after that, the state |n> represents the superposition state formed by L H-dimensional particles, such as |1> represents |00...1>, and the numbers in brackets correspond to the measurement results of each particle; the subscripts A and B represent their respective owners Alice and Bob; Step 2: Treat the two parts mentioned in step 1 as a whole system |ψ>0 According to the serial number, the multi-dimensional mixed state particle state is used as the control party and the shared state is used as the target to perform the control module addition operation on the mixed entangled state; each channel shared particle state is module added with the label of the corresponding control state, and this operation is named And act on the initial state: in Represents state n+i modulo H L addition; Step 3: In order to transmit the amplitude and phase information of the mixed superposition state through the channel, it is necessary to perform quantum Fourier transform of the corresponding dimensions on the K particles of the mixed state to be transmitted; the entire system is left with a channel entangled pair containing the phase information of the original multi-particle state and the controlled bit migration generated by the controlled unitary operation; after K Fourier transforms, the system becomes: Then the mixed particle state is measured separately and K measurement results d are obtained K d K-1 ...d1>, and The phase produced by the measurement is thus changed to: Step 4: Alice performs standard basis measurement on the shared particle pair she has, and based on the measurement result |m L m L- 1...m1> A The L H-dimensional particles owned by Bob are transformed into the form determined by the measurement results on both sides and written as In order to restore the form of expressing K mixed-dimensional particle states with L H dimensions, Bob needs to perform three different unitary operations corresponding to the measurement results. and Transform to restore; finally the result becomes: Each state pre-coefficient Represents the amplitude of the corresponding superposition state, the subscript L is the Lth particle shared by A and B, and each particle contains H possible dimensions; the above is the form of using H-dimensional particles to express mixed particle states of different dimensions; Step 5: In order to transform the multi-particle state obtained in the previous step into the original form, the receiver Bob needs to continue to perform controlled unitary operations on the restored multi-particle state and then measure it; K initial particles corresponding to the original multi-particle state need to be prepared as auxiliary particles for preparation; The system for the receiver to perform controlled unitary operation is written as: Where |0> k is the kth auxiliary particle introduced; imitate the construction of the controlled unitary in step 2, let the shared particle state part be the controller, and Bob's auxiliary particle part be the target, and act on the system composed of its L+K particles to perform the corresponding controlled unitary operation: And after Fourier transforming the L channel particles respectively, we get: in is the phase coefficient generated after Fourier transform; then measure it to get new L results |m L m L-1 ...m1> makes Bob's K mixed particle states become: Finally, the original K mixed entangled states are restored through the measurement results; The coefficients obtained Corresponding to the coefficients before transfer, |d1d2...d K > is its corresponding superposition state; The total number of states contained in the transmission channel is greater than the total number of states contained in the multi-particles to be transmitted, and the constraints that make the resources be used effectively; According to the serial number of each superposition state, the corresponding control modular addition operation is performed; by utilizing the unitary operation acting on particles of different dimensions, the conversion and recovery of dimensions between multi-particle states is realized.

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