Polarization-frequency two-degree-of-freedom encoding coherent state noiseless linear amplification method

Abstract

The application belongs to the technical field of quantum communication, and in particular relates to a polarization-frequency two-degree-of-freedom encoding coherent state noiseless linear amplification method. The parallel amplification idea is used. The original polarization-frequency two-degree-of-freedom encoded coherent state is split into N paths through a beam splitter array. The coherent state in each path becomes a weak coherent state. A PC amplifier and an auxiliary photon are arranged on each path. The photon state of each path is amplified. If all the PC amplifiers on all the paths operate successfully, the output states of all the amplifiers are converged on a path through another beam splitter array. Finally, a new coherent state is extracted. The application can effectively improve the average photon number in the output coherent state, realize amplification of the coherent state, and perfectly preserve the information of the photon encoding in the polarization and frequency two degrees of freedom. In addition, the application has strong practicability.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication technology, and particularly relates to noiseless linear amplification technology for coherent states. Specifically, it is a noiseless linear amplification method for coherent states encoded with polarization-frequency two degrees of freedom. Background Technology

[0002] Due to their high speed and ease of operation, photons have become the most commonly used information carrier in quantum communication. However, photons are susceptible to transmission loss due to channel noise when transmitting in practical quantum channels. Photon transmission loss reduces communication efficiency and even threatens communication security. Noiseless linear amplification (NLA) is an effective method to solve the photon transmission loss problem. By running an NLA scheme, the communicating party can probabilistically improve the fidelity of the target photon state. Common NLA schemes are based on quantum scissors (QS) technology. However, photocatalysis (PC) technology only requires half the number of beam splitters and single-photon detectors of QS technology to achieve NLA for low-energy input photon states. Moreover, PC technology has a higher success rate than QS technology. To achieve amplification of continuous-variable quantum states, Ralph et al. proposed the idea of ​​parallel QS or PC. The continuous-variable FOCK state is split into multiple paths by a beam splitter array, and a QS or PC amplifier is run on each path. Once all QS or PC amplifiers have successfully completed their operation, the output states of all amplifiers are converged onto a single path via a beam splitter array, thereby amplifying the FOCK state. In 2020, He et al. proposed an NLA scheme based on PC parallel processing of frequency degrees of freedom encoding coherent states. They demonstrated that PC-NLA requires fewer material resources than QS-NLA, and considering resource conservation and communication efficiency, the future development of PC-NLA is highly anticipated.

[0003] Coherent states are a special type of FOCK state with wide applications in quantum communication and quantum computing. In coherent states, the number of photons follows a Gaussian distribution. Multi-degree-of-freedom coding (hypercoding) of photons can effectively improve the channel capacity of photons and enhance the practical communication efficiency of quantum communication. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention discloses a PC parallel noiseless linear amplification scheme that protects coherent states encoded simultaneously in both polarization and frequency degrees of freedom. This scheme effectively increases the average number of photons in the output coherent states while perfectly preserving the encoded information of photons in both polarization and frequency degrees of freedom. The specific technical solution is as follows:

[0005] A noise-free linear amplification method for coherent states encoded by polarization-frequency two degrees of freedom specifically includes the following steps:

[0006] Step 1: Prepare a coherent state |α| that is simultaneously encoded in polarization and frequency degrees of freedom. FP >;

[0007] Step 2: Translate the coherent state |α FP >By splitting the beam into N spatial paths using a beam splitter array, the quantum states on each path decay into weakly coherent states;

[0008] Step 3: Set up a PC amplifier on each spatial path and prepare two polarization-frequency encoded auxiliary photons. The incident photon state and auxiliary photon state of each path enter the PC amplifier. If the PC amplifier on some paths does not get a successful detector response, discard all output states and the scheme terminates. If all PC amplifiers get a successful detector response, retain the output states on all paths and proceed to the next step.

[0009] Step 4: Input the output states of the PC amplifiers on the N paths into the second Nth-order beam splitter array, and measure the number of photons in all output registers of the beam splitter except for the first output port. When the number of photons in all the above registers is zero, the overall amplification scheme is successful, and the output photons of all paths will be converged into a single overall path output.

[0010] Step 5: Adjust the transmittance of the variable beam splitter within each PC amplifier. It can effectively increase the average number of photons in the total output state and achieve amplification of the coherent state.

[0011] A further improvement of the present invention is that: in step 1, the communication side prepares a coherent state encoded simultaneously in polarization and frequency degrees of freedom:

[0012]

[0013] Where 0, 1, 2…n… represent the number of photons, and α represents the average number of photons in the input coherent state:

[0014]

[0015] Where H and V represent the horizontal and vertical polarization of the photon, respectively, and ω1 and ω2 represent two different frequencies of the photon. The above equation indicates that each photon in the coherent state has the same encoding in both polarization and frequency degrees of freedom, and the encoding coefficients in the two degrees of freedom satisfy |γ1| 2 +|γ2| 2 =1,|δ0| 2 +|δ1| 2 =1, and all four coefficients are complex numbers.

[0016] In a further improvement of the present invention, in step 2, the communicating party splits the coherent state into N paths through the first beam splitter array and transmits it to the communicating party 2 through the quantum channel.

[0017] A further improvement to this invention is that the coherent state is split into N paths (N being relatively large) after passing through the first beam splitter array. The coherent state obtained on each path is a weakly coherent state, and its form is as follows:

[0018]

[0019] Since N is large, Therefore, we can ignore its higher-order terms and represent the above weakly coherent state as:

[0020] |α' FP >=C0|0>+C1|1 FP >,

[0021] in,

[0022] In a further improvement of the present invention, in step 3, one PC amplifier and two auxiliary photons are prepared for each path. The PC amplifier consists of two polarization beam splitters (PBS), two variable beam splitters (VBS) with a transmittance of T, and two Homodyne photon detectors. The function of the PBS is to completely transmit horizontally polarized photons (|H>) and completely reflect vertically polarized photons (|V>). The function of the VBS is to transmit photons with a probability of T and reflect photons with a probability of 1-T. When a photon with the quantum state γ1|ω1>+γ2|ω2> enters the Homodyne photon detector, the detector responds with a response probability of 100%. The quantum states of the two auxiliary photons are... This indicates that the two auxiliary photons have the same frequency encoding as the incident photon, and one photon has a polarization state of |H> and the other photon has a polarization state of |V>.

[0023] A further improvement to this invention is that within the PC amplifier, after the incident photon passes through the PBS, the horizontally polarized and vertically polarized photons enter the first and second branches, respectively. The photon in the first branch, along with an auxiliary photon of quantum state |H>(γ1|ω1>+γ2|ω2>), enters one VBS, and the photon in the second branch, along with an auxiliary photon of quantum state |V>(γ1|ω1>+γ2|ω2>), enters the second VBS. The PC amplifier operates successfully when each of the two Homodyne photon detectors detects one photon.

[0024] A further improvement of this invention is that, within the PC amplifier, when the input state is empty, only auxiliary photons enter the PC amplifier. Therefore, the total photon states of the PC amplifier are:

[0025]

[0026] In the above equation, only the term |H>5|V>7 will result in a successful detector response (each of the two Homodyne photon detectors detects one photon). When the input state is empty, the success probability of the PC amplifier is |C0|. 2 T 2 The output state is empty.

[0027] When the input state is a single-photon state, the input state and the auxiliary photon state enter the PC amplifier simultaneously. Therefore, the total number of photon states within the PC amplifier is:

[0028]

[0029] When the PC amplifier operates successfully, the above equation can be collapsed into:

[0030]

[0031] Finally, by passing the photons output from the first and second variable beam splitters through the second PBS, the output state of the PC amplifier when it succeeds can be obtained.

[0032] (δ0|H> 10 +δ1|V> 10 (γ1|ω1>+γ2|ω2>)=|1 FP > 10

[0033] The success probability of the PC amplifier is |C1| 2 T(2T-1) 2 As can be seen from the above equation, the output state perfectly preserves the encoding characteristics of the input state in both polarization and frequency degrees of freedom.

[0034] Therefore, the output state of each PC amplifier when it runs successfully is:

[0035]

[0036] make The output state can then be written as:

[0037]

[0038] P1 is the success probability of a single PC amplifier, and its form is:

[0039]

[0040] A further improvement of this invention is that, in step 4, when all PC amplifiers have successfully operated, the output states of all paths are converged onto one path through the second beam splitter array, while the outputs of the other paths are all 0. The resulting total output state is:

[0041]

[0042] P t The total success probability of this scaling-up scheme is expressed as:

[0043]

[0044] The output coherent state perfectly preserves the encoded information of the input coherent state in both polarization and frequency degrees of freedom. This can be achieved by adjusting the transmittance T of the VBS in the PC amplifier. available In this case, the average number of photons gα in the total output state is greater than the average number of photons α in the input coherent state, which means that the amplification is successful.

[0045] The beneficial effects of this invention are as follows: This invention can effectively increase the average number of photons in the output coherent state and perfectly preserve the coding information of photons in the two degrees of freedom of polarization and frequency in the coherent state. The devices used in this invention are all linear optical elements, which are feasible under current experimental conditions. Therefore, this solution has strong practicality. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the process of the present invention.

[0047] Figure 2 This is a schematic diagram of the PC amplifier of the present invention, wherein PBS represents a polarization beam splitter, VBS represents a variable beam splitter, and D1 and D2 are homodyne photon detectors.

[0048] Figure 3 This is a schematic diagram of the noiseless linear amplification scheme for polarization-frequency two-degree-of-freedom encoded coherent states of the present invention, where N-splitter represents a beam splitter array.

[0049] Figure 4 This is a graph showing the relationship between the total success probability and the amplification factor g of the noiseless linear amplification scheme for polarization-frequency two-degree-of-freedom encoded coherent states according to the present invention. Here, N represents the number of parallel amplification paths; we take N = 1, 2, 3, 4, 5, 6, 7, 8. Detailed Implementation

[0050] To enhance understanding of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are only used to explain the invention and do not limit the scope of protection of the invention.

[0051] Example:

[0052] The communicating party prepares a coherent state simultaneously encoded in polarization and frequency degrees of freedom, represented as follows:

[0053]

[0054] Where 0, 1, 2…n… represent the number of photons, and α represents the average number of photons in the input coherent state. This indicates that each photon in the coherent state has the same encoding in both polarization and frequency degrees of freedom. The encoding coefficients in both degrees of freedom satisfy |γ1| 2 +|γ2| 2 =1,|δ0| 2 +|δ1| 2 =1, and all four coefficients are complex numbers.

[0055] The communicating party splits the coherent state into N paths (N being relatively large) after passing it through the first beam splitter array. The coherent state obtained on each path is a weakly coherent state, and its form is as follows:

[0056]

[0057] Since N is large, its higher-order terms can be ignored, and the weakly coherent state can be represented as:

[0058] |α' FP >=C0|0>+C1|1 FP >,

[0059] in,

[0060] The communicating party feeds the signal state and auxiliary state of each path into the PC amplifier to run the amplification scheme. One PC amplifier and two auxiliary photons are prepared for each path. The PC amplifier consists of two polarization beam splitters (PBS), two variable beam splitters (VBS) with a transmittance of T, and two homodyne photon detectors. The PBS functions to completely transmit horizontally polarized photons (|H>) and completely reflect vertically polarized photons (|V>). The VBS functions to transmit photons with a probability of T and reflect photons with a probability of 1-T. The quantum state of the auxiliary photon in each path is... This indicates that the two auxiliary photons have the same frequency encoding as the incident photon, and one photon has a polarization state of |H> and the other photon has a polarization state of |V>.

[0061] When the input state of the PC amplifier is empty, only auxiliary photons enter the PC amplifier. Therefore, the total photon states of the PC amplifier are:

[0062]

[0063] In the above equation, only the term |H>5|V>7 will result in a successful detector response (hymodyne detectors D1 and D2 each detect one photon). When the input state is empty, the success probability of the PC amplifier is |C0|. 2 T 2 The output state is empty.

[0064] When the input state is a single-photon state |1 FP When >=[(γ1|ω1>+γ2|ω2>)(δ0|H>+δ1|V>)], after passing through the first PBS, the incident single-photon state becomes

[0065] |1 FP >→[(γ1|ω1>+γ2|ω2>)(δ0|H>2+δ1|V>3)]

[0066] The photon in the first branch, along with an auxiliary photon with the quantum state |H>(γ1|ω1>+γ2|ω2>), enters one VBS. The photon in the second branch, along with an auxiliary photon with the quantum state |V>(γ1|ω1>+γ2|ω2>), enters the second VBS. When each of the hymodyne detectors D1 and D2 detects one photon, the specific formula derivation process can be obtained as follows:

[0067]

[0068] Finally, by passing the photons output from the first and second variable beam splitters through the second PBS, the output state of the PC amplifier when it succeeds can be obtained as follows:

[0069] (δ0|H> 10 +δ1|V> 10 (γ1|ω1>+γ2|ω2>)=|1 FP > 10

[0070] The success probability of the PC amplifier is |C1| 2 T(2T-1) 2 As can be seen from the above equation, the output state perfectly preserves the encoding characteristics of the input state in both polarization and frequency degrees of freedom.

[0071] In summary, the output state of the PC amplifier when it is successfully operating is as follows:

[0072]

[0073] make The output state can then be written as:

[0074]

[0075] P1 is the success probability of a single PC amplifier, and its form is:

[0076]

[0077] When all PC amplifiers on all paths have successfully operated, the output states of all paths are converged onto one path via a second beam splitter array, while the outputs of the other output paths are all 0. The resulting total output state is:

[0078]

[0079] P t The total success probability of this coherent state parallel amplification scheme is expressed as:

[0080]

[0081] The output coherent state perfectly preserves the encoded information of the input coherent state in both polarization and frequency degrees of freedom. This is achieved by adjusting the transmittance T of the VBS in the PC amplifier. available In this case, the average number of photons gα in the total output state is greater than the average number of photons α in the input coherent state, which means that the amplification is successful.

[0082] A simulation graph is created to illustrate the relationship between the success probability and the amplification factor of this scheme. Since the success probability is very low when the amplification factor is large, the success probability P is taken as the logarithm to the base 10 to more clearly demonstrate the relationship. The results are as follows when the number of paths N ranges from 1 to 8: Figure 4 As shown, the conclusion is that the success probability of this scheme decreases as the amplification factor increases. This means that in practical applications, we need to consider both the success probability and the amplification factor when setting the experimental parameters. Furthermore, the larger the number of beam splitting paths N, the lower the overall success probability of the scheme.

[0083] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for noise-free linear amplification of coherent states using polarization-frequency two-degree-of-freedom encoding, characterized in that, Specifically, the following steps are included: Step 1: Prepare a coherent state |α| that is simultaneously encoded in polarization and frequency degrees of freedom. FP >; Step 2: Translate the coherent state |α FP >By splitting the beam into N spatial paths using a beam splitter array, the quantum states on each path decay into weakly coherent states; Step 3: Set up a PC amplifier on each spatial path and set up two polarization-frequency encoded auxiliary photons. The PC amplifier consists of two polarization beamsplitters, two variable beamsplitters with a transmittance of T, and two homodyne photon detectors. After the incident photons pass through the polarization beamsplitters, the horizontally polarized photons and the vertically polarized photons enter the first branch and the second branch, respectively. The photons in the first branch and the auxiliary photons with the quantum state |H>(γ1|ω1>+γ2|ω2>) enter the first variable beamsplitter. The photons in the second branch and the auxiliary photons with the quantum state |H>(γ1|ω1>+γ2|ω2>) enter the first variable beamsplitter. An auxiliary photon with quantum state |V>(γ1|ω1>+γ2|ω2>) enters the second variable beam splitter. When each of the two homodyne photon detectors detects a photon, the PC amplifier operates successfully. The incident photon state and auxiliary photon state of each path enter the PC amplifier. If the PC amplifier on some paths does not get a successful detector response, all output states are discarded and the scheme terminates. If all PC amplifiers get a successful detector response, the output states on all paths are retained and the next step is performed. Step 4: Input the output states of the photocatalytic PC amplifiers on the N paths into the second Nth-order beam splitter array, and measure the number of photons in all registers of the beam splitter except for the first output port. When the number of photons in all the above registers is zero, the overall amplification scheme is successful, and the output photons of all paths will be converged into a single overall path output. Step 5: Adjust the transmittance of the variable beam splitter in each PC amplifier to increase the average number of photons in the total output state and achieve amplification of the coherent state.

2. The polarization-frequency two-degree-of-freedom encoded coherent state noiseless linear amplification method according to claim 1, characterized in that, In step 1, the communication side prepares coherent states that are simultaneously encoded in polarization and frequency degrees of freedom: Where 0, 1, 2…n… represent the number of photons, and α represents the average number of photons in the input coherent state: Where H and V represent the horizontal and vertical polarization of the photon, respectively, and ω1 and ω2 represent two different frequencies of the photon. The above equation indicates that each photon in the coherent state has the same encoding in both polarization and frequency degrees of freedom, and the encoding coefficients in the two degrees of freedom satisfy |γ1| 2 +|γ2| 2 =1,|δ0| 2 +|δ1| 2 =1, and all four coefficients are complex numbers.

3. The polarization-frequency two-degree-of-freedom encoded coherent state noiseless linear amplification method according to claim 1, characterized in that, After passing through the first beam splitter array, the coherent state is divided into N paths. The coherent state obtained on each path is a weakly coherent state, and its form is as follows: The weakly coherent states described above can be represented as follows: |a' FP >=C0|0>+C1|1 FP >, in, 4. The polarization-frequency two-degree-of-freedom encoded coherent state noiseless linear amplification method according to claim 3, characterized in that, In step 3, the total photon states within the PC amplifier are: In the above formula, only the term |H>5|V>7 will result in a successful detector response. When the input state is empty, the success probability of the PC amplifier is |C0|. 2 T 2 The output state is empty; When the input state is a single-photon state, the input state and the auxiliary photon state enter the PC amplifier simultaneously. Therefore, the total number of photon states within the PC amplifier is: When the PC amplifier operates successfully, the above equation can be collapsed into: Finally, the photons output from the first and second variable beam splitters are passed through the second polarization beam splitter to obtain the output state of the PC amplifier when it succeeds: (δ0|H> 10 +δ1|V> 10 )(γ1|ω1>+γ2|ω2>)=|1 FP > 10 The success probability of the PC amplifier is |C1| 2 T(2T-1) 2 The output state of each PC amplifier when it runs successfully is as follows: make The output state can then be written as: P1 is the success probability of a single PC amplifier, and its form is:

5. The polarization-frequency two-degree-of-freedom encoded coherent state noiseless linear amplification method according to claim 4, characterized in that, In step 4, when all PC amplifiers have successfully operated, the output states of all paths are converged onto one path through the second beam splitter array, while the outputs of the other paths are all 0. The resulting total output state is: P t The total success probability of this scaling-up scheme is expressed as: The output coherent state perfectly preserves the encoded information of the input coherent state in both polarization and frequency degrees of freedom. This can be achieved by adjusting the transmittance T of the variable beam splitter in the PC amplifier. get In this case, the average number of photons gα in the total output state is greater than the average number of photons α in the input coherent state, which means that the amplification is successful.

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