A high-capacity teleportation method based on three-dimensional electron-photon entangled state

Abstract

This invention discloses a high-capacity teleportation method based on three-dimensional electron-photon entangled states: Step 1: Alice prepares electron-photon entangled pairs and splits them into photon sequences. P and electronic sequence E Step 2: Alice sequences the electrons. E Send to Bob; Step 3: Alice selects the unitary operation and applies it to the photon sequence. P Bob obtains the photon sequence and the electron sequence; Step 4: Bob uses phase-shifting electron holography to perform interferometric measurements on the electron sequence and acquires an interference hologram; Step 5: Bob informs Alice to measure the photon sequence and provides her with the photon number, state, and position; Step 6: Bob performs phase reconstruction on the interference hologram and decodes the original information. This invention, through a rationally designed coding phase interval and by controlling the extremely low decoding failure rate with a confidence coefficient, surpasses the theoretical limit of 2log23 bits for the coding capacity of traditional 3D photon Bell state ultra-dense coding, achieving a theoretical coding capacity of 8.5 bits with a bit error rate of 0.27%.

Description

Technical Field

[0001] This invention belongs to the field of quantum teleportation technology, specifically relating to a high-capacity teleportation method based on three-dimensional electron-photon entangled states. Background Technology

[0002] Quantum teleportation is a key technology that combines quantum entanglement with classical communication to achieve non-local transmission of unknown quantum states in space. Its core lies in not directly transmitting the physical particle itself, but rather "decomposing" the information carried by the quantum state and reconstructing it at another location to obtain the information. As a fundamental and applied research direction in quantum information science, it has become one of the key technologies for building long-distance quantum networks and supporting distributed quantum computing.

[0003] Reference 1, “Zhang CY, Zheng ZJ, Fan ZB, et al. The efficiency of quantum teleportation with three-qubit entangled state in a noisy environment[J].Scientific Reports, 2023, 13(1): 3756”, proposes to use the maximally entangled state of a four-level quantum system as a quantum channel to realize quantum teleportation. A single four-level maximally entangled pair can transmit 4 bits of classical information.

[0004] Reference 2, "Kazakevich E, Aharon H, Kfir O. Spatial electron-photonentanglement[J]. Physical Review Research, 2024, 6(4): 043033", utilizes the entanglement of the two-path spatial superposition state of free electrons with the two-mode photons to realize a spatially encoded electron-photon entanglement scheme based on path degrees of freedom. However, the theoretical limit of the two-dimensional spatial degrees of freedom encoding capacity of this scheme is 1 qubit.

[0005] The encoding capacity of the aforementioned existing schemes is limited by their finite entanglement resources. d of Theoretically, low-dimensional entanglement resources cannot support multiple qubits, which severely limits the number of distinguishable entangled states. Therefore, how to overcome the limitations of existing entanglement dimensions has become a key problem that urgently needs to be solved in quantum teleportation technology. Summary of the Invention

[0006] The purpose of this invention is to provide a high-capacity teleportation method based on three-dimensional electron-photon entangled states, so as to improve the coding capacity in three-dimensional entangled states.

[0007] To achieve the above objectives, the present invention employs the following technical solution:

[0008] A high-capacity teleportation method based on three-dimensional electron-photon entangled states includes the following steps: Step 1: Alice prepares a set of electron-photon entangled pairs as quantum signals, and then splits these electron-photon entangled pairs into two sequences, one of which is called the photon sequence. P Another group is called the electronic sequence. E ; Step 2: Alice uses the electronic sequence prepared in Step 1 E The photon sequence was sent to Bob via a quantum channel and stored. P ; Step 3: Alice, based on the information to be transmitted, selects from the preset unitary operation family { In the sequence, select the corresponding unitary operation and apply it sequentially to the photon sequence of the electron-photon entangled states it holds. P By leveraging the nonlocality of quantum entanglement, information is mapped to specific relative phases between electronic energy level states, thereby completing the encoding and obtaining a photon sequence. Bob obtained the electronic sequence ; Step 4: Bob uses phase-shifting electron holography to analyze the electron sequence. Perform interferometry, according to the electronic sequence Sequentially, the position of each electronic energy level state on the interference hologram is recorded at the measurement end; by changing the electronic sequence... By adjusting the tilt angle, a series of interferometric holograms with different initial phase shifts were acquired; Step 5: After Bob completes the measurement in Step 4, he informs Alice to measure the photon sequence he has saved. And the measurement results of each photon number state and its position in the photon sequence The location information is communicated to Bob via the classic channel; Step 6: Bob performs phase reconstruction on the interference hologram obtained in Step 4 to obtain the experimentally measured phase value of each electronic level state relative to the reference state. Bob compares each measured phase with multiple fault-tolerant phase intervals preset based on the system phase noise. If the measured phase falls within a certain fault-tolerant phase interval, he compares the fault-tolerant phase interval with the photon number state of the corresponding measured phase provided by Alice to uniquely determine the unitary operation used, thereby decoding the original information. If the measured phase falls outside all fault-tolerant phase intervals, he determines that the current information decoding has failed.

[0009] Furthermore, in step 1, the electron-photon entangled pair prepared by Alice is as follows:

[0010] in, It is the initial state loss of electrons n The state after the energy of one photon; It is the photon number state; Corresponding to the Poisson scattering probability, where It is the vacuum coupling strength. n !yes n factorial.

[0011] Furthermore, in step 3, the preset family of unitary operations { }for:

[0012] in, , k It is a positive integer. d For the electron-photon entangled state dimension, ; Let be the basis vectors of the photon number state space. It is a projection operator on the number state of photons; Q It is the phase manipulation factor, a positive integer, satisfying... ,in z , is the confidence coefficient This is the phase resolution.

[0013] Furthermore, in step 3, the selected unitary operation is applied sequentially to the photon sequence of its held electron-photon entangled states. P The above form is as follows:

[0014] in, It is the unit operator for the electronic part; It belongs to the unitary operation family of the photon part.

[0015] Furthermore, in step 3, the encoding rule is: Alice will perform the unitary operation. according to k Value size, and unitary operations Encoded as k -1 corresponds to binary information; Alice's photon sequence P Apply unitary operation Because electrons and photons are in an entangled state, this operation utilizes the non-local correlation of quantum entanglement to... k The binary information corresponding to -1 is encoded as a specific relative phase distribution between electronic energy levels, making the electronic energy level states and Relative phase factor is generated between them .

[0016] Furthermore, in step 4, for phase-shifting electron holography, the entanglement pairs of electron-photon entangled states... No phase change is introduced by any unitary operation, and the electronic energy level state It maintains good coherence with other superimposed electronic energy level states, therefore, in phase-shifting electron holography, the selected electronic energy level state... As a reference wave, the remaining energy levels are treated as object waves; using a double-prism to form an interference hologram reduces Fresnel diffraction at the electron double-prism, and the double-prism can be set in the measuring instrument before measurement; in the electron sequence A magnetic prism spectrometer is positioned before the electron biprism to separate the reference wave and the object wave. After collimation using a magnetic lens, the electron sequence is then... Interference is achieved by inputting an electronic biprism.

[0017] Furthermore, in step 6, when performing phase reconstruction on the interferometric hologram obtained in step 4, the first... t An interferometric hologram at position ( x , y Intensity distribution at () for:

[0018] Where A(x,y) and Represents the amplitude and phase of an electron wave; T x and T y express x and y The spacing of interference fringes in the direction; B t and C t They represent the first t Average intensity and fringe contrast of each interference hologram; It is the initial phase of the first hologram. It is the first t The initial phase of each hologram; the complex form of this formula is:

[0019] in,

[0020] Therefore, the electronic energy level states encoded by unitary operations Relative to the reference state The experimentally measured phase is: .

[0021] Furthermore, in step 6, under multi-amplitude phase-shifted electron holography, shot noise becomes the dominant noise limiting phase resolution, while other noises are negligible under statistical averaging. N When sufficiently large, it can be approximated as a Gaussian distribution using the central limit theorem. In this case, the standard deviation is reconstructed using the phase. Describing this phase noise as the phase resolution, then measuring the phase... satisfy:

[0022] in, n It is the number of photons in the photon number state corresponding to this phase. , k It is the unitary operation control factor. Q It is a phase control factor; in the confidence coefficient z Under the premise that the preset fault-tolerant phase interval is expressed as: .

[0023] Compared with the prior art, the present invention has the following technical advantages: (1) In the encoding stage, the present invention uses the electron-photon entangled state as the quantum channel and the free electron energy level state as the information carrier. By designing a family of unitary operations with a specific phase structure to act on the photon part of this entangled state, the relative phase is introduced between the electron energy levels by utilizing the nonlocality of quantum entanglement to complete the encoding. (2) In the decoding stage, the present invention uses phase-shifting electronic holography as a measurement method, and uses the intrinsic electronic ground state as a reference wave for interferometric measurement. By reasonably designing the coding phase interval, it ensures that the tolerance phase intervals of each codeword do not overlap, thereby completing the decoding by controlling the extremely low bit error rate through the confidence coefficient. In summary, this invention is the first to employ electron-photon entanglement as a quantum channel, using free electrons as information carriers, designing a specific family of unitary operations for encoding, and employing phase-shifting electron holography for decoding. When using three-dimensional electron-photon entanglement, a maximum encoding capacity of 8.5 bits was achieved with a bit error rate of only 0.27%, far exceeding traditional methods. d The theoretical limit of the coding capacity of 2log2d bits for ultra-dense coding of dimensional photonic Bell states. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the principle of the present invention, wherein, It is the initial state of electron-photon entanglement. P It is the initial photon sequence. E It is the initial electron sequence. P' It is the encoded photon sequence.E' It is the encoded electronic sequence.

[0025] Figure 2 A comparison diagram of the encoding capacity-dimensionality relationship between electron-photon entangled states and photonic Bell states, where, C For encoding capacity, d Entangled state dimension C 1 is d The upper limit of the coding capacity of a dimensional photonic Bell state. C 2 is the confidence coefficient of this invention. z The upper limit of the encoding capacity when =3, data1 is the intersection of the two curves. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and embodiments, so that those skilled in the art can better understand the present invention.

[0027] This embodiment discloses a high-capacity teleportation method based on three-dimensional electron-photon entangled states, taking a confidence coefficient. z =3, to ensure that the tolerance phase intervals do not overlap, the phase manipulation factor is taken as 3. Q =17, encoding and decoding 4 bits of information with a bit error rate of 0.27%, the method includes the following steps: Step 1: Alice Preparation N A three-dimensional electron-photon entangled pair, namely , will this N Each entangled pair is divided into a photon sequence. P ={P i} and the electronic sequence E={E i}, and i∈[1,N].

[0028] Step 2: Alice sequences the electrons E The photon sequence was sent to Bob via a quantum channel and stored. P .

[0029] Step 3: Alice, based on the information to be transmitted, selects from the preset unitary operation family { Select the "you" operation in} k=1, 2, ..., 16, and the selected unitary operations are applied sequentially to the photon sequences they hold. P The information is mapped to a specific relative phase between electronic energy level states, thereby completing the encoding and obtaining a photon sequence. Bob obtained the electronic sequence .

[0030] Step 4: Bob uses phase-shifting electron holography to process the received electron sequence. To perform interferometry, before the electron sequence enters the electron biprism, a magnetic prism spectrometer separates the reference wave and the object wave, and after collimation by a magnetic lens, the signal is input into the electron biprism for interference; according to the electron sequence... Sequence, record the number i The position of each electronic energy level state on the interference hologram (x i ,y i By changing the incident tilt angle of the electron sequence, a series of electron interference holograms with different initial phase shifts are acquired.

[0031] Step 5: After Bob completes the interferometry, he informs Alice to measure the photon sequence he has saved. And the measurement results of each photon number state and its position in the photon sequence Bob is informed of the location via a classical channel.

[0032] Step 6: Bob performs phase reconstruction on the obtained interference hologram to obtain... N The intensity distribution expression of the first hologram, t ( Intensity distribution of amplitude At position x=x i y=y i The intensity data are as follows:

[0033] pass N A hologram at position (x) i ,y i The measured phase at this location is obtained by averaging multiple images:

[0034] in, .

[0035] Step 7: When the confidence coefficient z =3, phase resolution At that time, the theoretical tolerance phase interval with no phase overlap is preset as follows: ,in, , Bob will measure each phase. The measured phase is compared with the fault-tolerant phase interval. If the measured phase falls within a certain fault-tolerant phase interval, this interval is jointly compared with the photon number state corresponding to the measured phase provided by the sender to uniquely determine the unitary operation used. The original information is decoded with a theoretical probability of 99.73%. If the measured phase falls outside all fault-tolerant phase intervals, the current information decoding is determined to have failed with a theoretical probability of 0.27%.

[0036] The following is an analysis of the encoding capacity of this invention: To ensure that the tolerance phase intervals do not overlap and to prevent phase entanglement, the parameters of this invention must satisfy the following relationship:

[0037] In phase-shifting electron holography, the phase follows a Gaussian distribution, and when the phase resolution... By selecting the corresponding confidence coefficient z according to different bit error rate standards, multi-dimensional coding adjustment can be achieved. For a bit error rate of 0.27%, the confidence coefficient z is... z =3, calculated from the inequality above. Q The maximum value is 361, which is the unitary operation control factor. k satisfy: When satisfied At that time, this invention surpasses the standard in entanglement dimensions of 3 to 9 dimensions. d The theoretical limit of 2log2d bits for ultra-dense coding of 3D photonic entangled Bell states is shown, with lower dimensionality resulting in higher coding capacity. When using 3D electron-photon entangled states, a theoretical coding capacity of 8.5 bits can be achieved with a bit error rate of 0.27%, which is 1.68 times higher than the theoretical limit of 3D photonic entangled Bell states. A comparison of their coding capacity versus dimensionality curves is shown below. Figure 2 As shown.

Claims

1. A high-capacity teleportation method based on three-dimensional electron-photon entangled states, characterized in that, Includes the following steps: Step 1: Alice prepares a set of electron-photon entangled pairs as quantum signals, and then splits these electron-photon entangled pairs into two sequences, one of which is called the photon sequence. P Another group is called the electronic sequence. E ; Step 2: Alice uses the electronic sequence prepared in Step 1 E The photon sequence was sent to Bob via a quantum channel and stored. P ; Step 3: Alice, based on the information to be transmitted, selects from the preset unitary operation family { In the sequence, select the corresponding unitary operation and apply it sequentially to the photon sequence of the electron-photon entangled states it holds. P By leveraging the nonlocality of quantum entanglement, information is mapped to specific relative phases between electronic energy level states, thereby completing the encoding and obtaining a photon sequence. Bob obtained the electronic sequence ; Step 4: Bob uses phase-shifting electron holography to analyze the electron sequence. Perform interferometry, according to the electronic sequence Sequentially, the position of each electronic energy level state on the interference hologram is recorded at the measurement end; by changing the electronic sequence... By adjusting the tilt angle, a series of interferometric holograms with different initial phase shifts were acquired; Step 5: After Bob completes the measurement in Step 4, he informs Alice to measure the photon sequence he has saved. And the measurement results of each photon number state and its position in the photon sequence The location information is communicated to Bob via the classic channel; Step 6: Bob performs phase reconstruction on the interference hologram obtained in Step 4 to obtain the experimentally measured phase value of each electronic level state relative to the reference state. Bob compares each measured phase with multiple fault-tolerant phase intervals preset based on the system phase noise. If the measured phase falls within a certain fault-tolerant phase interval, he compares the fault-tolerant phase interval with the photon number state of the corresponding measured phase provided by Alice to uniquely determine the unitary operation used, thereby decoding the original information. If the measured phase falls outside all fault-tolerant phase intervals, he determines that the current information decoding has failed.

2. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 1, the electron-photon entangled pair prepared by Alice is as follows: in, It is the initial state loss of electrons n The state after the energy of one photon; It is the photon number state; Corresponding to the Poisson scattering probability, where It is the vacuum coupling strength. n !yes n factorial.

3. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 3, the preset family of unitary operations { }for: in, , k It is a positive integer. d For the electron-photon entangled state dimension, ; Let be the basis vectors of the photon number state space. It is a projection operator on the number state of photons; Q It is the phase manipulation factor, a positive integer, satisfying... ,in z , is the confidence coefficient This is the phase resolution.

4. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 3, the selected unitary operation is applied sequentially to the photon sequence of its held electron-photon entangled states. P The above form is as follows: in, It is the unit operator for the electronic part; It belongs to the unitary operation family of the photon part.

5. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 3, the encoding rule is: Alice will perform the unitary operation. according to k Value size, and unitary operations Encoded as k -1 corresponds to binary information; Alice's photon sequence P Apply unitary operation Because electrons and photons are in an entangled state, this operation utilizes the non-local correlation of quantum entanglement to... k The binary information corresponding to -1 is encoded as a specific relative phase distribution between electronic energy levels, making the electronic energy level states and Relative phase factor is generated between them .

6. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 4, electronic energy level states are selected in phase-shifting electron holography. As a reference wave, the remaining energy levels are treated as matter waves; an interference hologram is formed using a double-double prism; in the electron sequence A magnetic prism spectrometer is positioned before the electron biprism to separate the reference wave and the object wave. After collimation using a magnetic lens, the electron sequence is then... Interference is achieved by inputting an electronic biprism.

7. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 6, when performing phase reconstruction on the interferometric hologram obtained in step 4, the first... t An interferometric hologram at position ( x , y Intensity distribution at () for: Where A(x,y) and Represents the amplitude and phase of an electron wave; T x and T y express x and y The spacing of interference fringes in the direction; B t and C t They represent the first t Average intensity and fringe contrast of each interference hologram; It is the initial phase of the first hologram. It is the first t The initial phase of each hologram; the complex form of this formula is: in, Therefore, the electronic energy level states encoded by unitary operations Relative to the reference state The experimentally measured phase is: 。 8. The high-capacity teleportation method based on three-dimensional electron-photon entangled states as described in claim 1, characterized in that, In step 6, under multi-amplitude phase-shifted electron holography, shot noise becomes the dominant noise limiting phase resolution, while other noises are negligible under statistical averaging. N When sufficiently large, it can be approximated as a Gaussian distribution using the central limit theorem. In this case, the standard deviation is reconstructed using the phase. Describing this phase noise as the phase resolution, then measuring the phase... satisfy: in, n It is the number of photons in the photon number state corresponding to this phase. , k It is the unitary operation control factor. Q It is a phase control factor; in the confidence coefficient z Under the premise that the preset fault-tolerant phase interval is expressed as: .

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