Loop-assisted quantum state amplifier and design method thereof

Abstract

The invention discloses a loop-assisted quantum state amplifier. The loop-assisted quantum state amplifier comprises a quantum state amplification module and a photon subtraction module, the quantum state amplification module adds any input coherent state into thermal noise to cause random displacement transformation of the coherent state to obtain a Gaussian mixture output state; the photon subtraction module comprises a beam splitter, a single-photon detector and quantum optical switches at the two ends of the beam splitter, the vacuum state and the output state of the quantum state amplification module are coupled at the beam splitter, single-photon subtraction is executed, photons are detected at the beam splitter through the single-photon detector, if the photons are detected, the amplified quantum state is output, and otherwise, the photon subtraction module outputs the amplified quantum state. And the quantum optical switch transfers the quantum state into the loop, and photon subtraction is executed again. According to the scheme, a feedback loop is added in the photon subtraction step, and when detection fails, the quantum state is allowed to enter the loop and the photon subtraction operation is repeated. Therefore, the success rate of the quantum amplifier is obviously improved, and meanwhile, the decoherence of the quantum state is also reduced.

Description

Technical Field

[0001] The present invention belongs to the field of quantum optics, and in particular relates to a loop-assisted quantum state amplifier and a design method thereof. Background Art

[0002] In quantum information processing, the inevitable loss in the channel and various noises that may exist in the experiment will not only cause the decoherence of the quantum state and the loss of quantum information, reducing communication efficiency, but also reduce the accuracy of phase measurement and increase phase uncertainty. Phase-insensitive noiseless quantum probability amplification technology is one of the important tools to solve these problems. A key advantage of this quantum amplifier is that it can introduce almost no additional noise while amplifying the quantum state. In practical applications, it can be used to enhance the reliability of quantum communication. At the same time, due to the improvement of phase measurement accuracy, it is also crucial for applications such as precision measurement, quantum sensing and quantum metrology.

[0003] In 2009, Ralph et al. proposed a method for noiseless amplification using a single-photon detector and an auxiliary single-photon source. This amplifier is referred to as NLA (Noiseless linear amplifier). This method has attracted widespread attention since it was proposed. Before this, phase-insensitive quantum amplifiers could not avoid the introduction of noise when acting on quantum states. The emergence of NLA shows that noiseless probability amplification of quantum states is possible. Later, based on the scheme of Ralph et al., researchers tried to apply various methods, such as combining teleportation, optimal entanglement exchange and multiplexed quantum error correction schemes. However, due to the need for non-Gaussian resources and operations, it is technically difficult to implement in experiments. Therefore, many other methods with the same amplification effect have been proposed one after another.

[0004] One method is to simulate NLA by adding a post-selection filter function after measurement. The theory of this method was proposed in 2012 and realized experimentally two years later. Then it was combined with deterministic quantum amplifiers, probabilistic cloning proofs, and thermal decoherence suppression. The post-selection function needs to set a cutoff value. When the cutoff value takes a variable value related to the total number of measurements, the rejection rate of the measurement data increases with the increase of the total number of measurements. Although the simulation degree is good, the experimental efficiency is low; when the cutoff value is a fixed value, the post-selection operation is more efficient but the simulation degree is lower, and the safety analysis is more complicated. Another method boldly adds thermal noise to the signal state and combines it with photon subtraction to complete the effective amplification of the quantum state. Because the scheme is cleverly designed and does not require non-Gaussian resources, someone completed the corresponding experimental work in the same year. However, the success probability of this scheme is very low, only a few percent. In order to obtain higher fidelity and effective amplification gain, a noiseless amplification scheme based on the combination of single-photon addition and subtraction was proposed, and it was improved to only need to combine photon subtraction with auxiliary Gaussian compression Gaussian vacuum state. The third type of method is to use quantum state comparison to amplify quantum states. By comparing the similarities or differences between two or more quantum states, the quantum states that meet the specific phase relationship are retained after selection, thereby achieving quantum state amplification without additional noise. Quantum state comparison can also be combined with other quantum operations (such as photon addition or subtraction) to further enhance the amplification effect. However, this method relies on multiple repeated measurements and post-selection, which requires a large amount of auxiliary resource states, increasing the resource requirements of the experiment. These quantum amplification schemes are inherently probabilistic, so improving the probability of success and amplification gain are important research directions to improve the practical usability and scalability of quantum amplification schemes.

[0005] Among these quantum amplification schemes, the quantum amplifier scheme that combines thermal noise and photon subtraction is particularly worthy of attention. This scheme can achieve noise-free phase information amplification without using any non-classical resources or strong parameter interactions. Although researchers have proposed many methods to improve this amplification scheme and improve system performance such as fidelity and amplification gain, these schemes have also achieved certain success in theory and experiment. However, they all propose new amplifier scheme designs and do not attempt to solve the key problem that this quantum amplifier scheme has good amplification performance but a low probability of success. Especially in the original scheme, when using multi-photon subtraction operations, as the number of subtracted photons increases, the success rate will decrease rapidly and become closer to zero. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a loop-assisted quantum state amplifier and a design method thereof, which solves the problem in the prior art that when using multi-photon subtraction operation, the success rate decreases rapidly as the number of subtracted photons increases.

[0007] The present invention adopts the following technical solutions to solve the above technical problems:

[0008] A loop-assisted quantum state amplifier comprises a quantum state amplification module and a photon subtraction module; the quantum state amplification module adds thermal noise to an arbitrary coherent state input, resulting in a random displacement transformation of the coherent state, and obtains a Gaussian mixed output state; the photon subtraction module comprises a beam splitter, a single-photon detector, and a quantum optical switch at both ends of the beam splitter; a vacuum state is coupled with an output state of the quantum state amplification module at the beam splitter, single-photon subtraction is performed, and photons are detected at the beam splitter using the single-photon detector; if photons are detected, the amplified quantum state is output; otherwise, the quantum optical switch transfers the quantum state into the loop and re-executes the photon subtraction.

[0009] The loop has a preset maximum number of cycles.

[0010] The maximum number of cycles is determined according to the success probability and the amplification effect.

[0011] As the maximum number of cycles increases, the corresponding optimal thermal noise decreases.

[0012] The design method of the loop-assisted quantum state amplifier comprises the following steps:

[0013] Step 1: Take any coherent state Add thermal noise, which causes random displacement transformation of the coherent state, and obtain the output state;

[0014] Step 2: Vacuum Coupled with the output state of step 1 at the beam splitter to perform single-photon subtraction;

[0015] Step 3: Use a single photon detector to detect photons at the beam splitter coupling point. If the photons are successfully detected, the quantum state of the amplified output is directly obtained; otherwise, execute step 4;

[0016] Step 4: Determine whether the number of cycles is greater than the maximum preset value. If not, re-enter the quantum state after the detection failure into the loop, perform photon subtraction, and return to step 3; otherwise, discard the quantum state.

[0017] A quantum optical switch is used to transfer the quantum state after detection failure back into the loop.

[0018] In step 1, the coherent state The density matrix after adding thermal noise is expressed as:

[0019]

[0020] in, , is the amplitude of the input coherent state, is the integration variable, is the number of thermal noise photons, is a complex variable Elements of the double integral in the complex plane.

[0021] After successful detection without loops, the density matrix of the output state becomes:

[0022]

[0023] in, , is the transmittance of the beam splitter,

[0024] The predicted success probability is .

[0025] In step 4, When the next cycle detection is successful, the density matrix of the quantum state is:

[0026]

[0027] in, , The transmittance of the beam splitter obtained by equivalently modeling the inefficient optical switch, is the corresponding success probability.

[0028] After averaging all the possible numbers of successful detection loops, the success probability is , the density matrix of the final state is obtained as:

[0029] .

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. The scheme adds a feedback loop to the photon subtraction step, allowing the quantum state to enter the loop and repeat the photon subtraction operation when the detection fails. The experimental results show that after adding the loop, the success rate of the quantum amplifier has been significantly improved, and the decoherence of the quantum state has also been reduced.

[0032] 2. Under different conditions, the lowest phase variance can be achieved by selecting the optimal noise parameters. The impact of the non-ideality of real photon detectors and optical switches on amplifier performance is studied, which provides new possibilities for the practical application and scalability of quantum amplification technology and lays the foundation for the future development of quantum information technology.

[0033] 3. The quantum amplifier model composed of thermal noise and photon subtraction does not require any non-Gaussian resources or strong parameter interactions, can achieve noise-free phase information amplification, and the technology required for the experiment is simple.

[0034] 4. The addition of the loop can realize a quantum state amplification process with a higher success probability and less quantum decoherence. The loop-assisted quantum amplifier has been proven to have better practical performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The maximum number of cycles of the present invention is different performance changes under .

[0036] Figure 2 is the number of different thermal noise photons in the present invention The standard deviation under .

[0037] Figure 3 This is a schematic diagram of the loop-assisted quantum state amplifier of the present invention. DETAILED DESCRIPTION

[0038] The structure and working process of the present invention will be further described below in conjunction with the accompanying drawings.

[0039] The purpose of the present invention is to address the problem that the current quantum amplifier basic model including thermal noise and photon subtraction has a good amplification effect, but a low success probability and low practical feasibility. A design and implementation method of a quantum state probability amplifier combining loop-assisted thermal noise and photon subtraction is proposed, and the amplifier design has been proven to have better practical performance. This scheme is based on a quantum amplifier model composed of thermal noise and photon subtraction, and loop assistance is introduced in the photon subtraction module, thereby a quantum amplifier with a higher success probability and less quantum decoherence is designed.

[0040] Due to channel loss and possible losses in various experiments, the decoherence of quantum states has greatly limited long-distance communications, especially for continuous variables. In addition to reducing quantum decoherence, another indicator that should be taken into account in experiments is the probability of success. The higher the probability of success, the more practical the scheme is and the more likely it is to be successfully applied in reality. Therefore, for a continuous variable quantum amplifier scheme, we should not only pay attention to the amplification gain of the output state, but also the success rate and degree of decoherence are important aspects of measuring the performance of the scheme.

[0041] A loop-assisted quantum state amplifier comprises a quantum state amplification module and a photon subtraction module; the quantum state amplification module adds thermal noise to an input arbitrary coherent state, thereby causing a random displacement transformation of the coherent state and obtaining a Gaussian mixed output state; the photon subtraction module comprises a beam splitter, a single-photon detector, and a quantum optical switch at both ends of the beam splitter; a vacuum state is coupled with an output state of the quantum state amplification module at the beam splitter to perform single-photon subtraction, and a single-photon detector is used to detect photons at the beam splitter; if a photon is detected, an amplified quantum state is output; otherwise, the quantum optical switch transfers the quantum state into the loop and re-executes photon subtraction.

[0042] Specific embodiments, such as Figure 3 As shown,

[0043] The loop-assisted quantum state amplifier comprises a quantum state amplification module and a photon subtraction module which are arranged in sequence; the quantum state amplification module converts any coherent state of the input After adding thermal noise, it causes random displacement transformation of the coherent state, and obtains a Gaussian mixed output state; the photon subtraction module includes a beam splitter BS, a single photon detector APD, and a quantum optical switch os at both ends of the beam splitter BS. The vacuum state and the output state of the quantum state amplification module are coupled at the beam splitter BS to perform single-photon subtraction. The single-photon detector APD is used to detect photons at the beam splitter. If a photon is detected, the amplified quantum state is output, otherwise, the quantum optical switch transfers the quantum state into the loop and re-executes photon subtraction.

[0044] The design method of the loop-assisted quantum state amplifier comprises the following steps:

[0045] Step 1: Take any coherent state Add thermal noise, which causes random displacement transformation of the coherent state, and obtain the output state;

[0046] Step 2: Vacuum Coupled with the output state of step 1 at the beam splitter to perform single-photon subtraction;

[0047] Step 3: Use a single photon detector to detect photons at the beam splitter coupling point. If the photons are successfully detected, the quantum state of the amplified output is directly obtained; otherwise, execute step 4;

[0048] Step 4: Determine whether the number of cycles is greater than the maximum preset value. If not, re-enter the quantum state after the detection failure into the loop, perform photon subtraction, and return to step 3; otherwise, discard the quantum state.

[0049] Specific embodiments, such as Figure 1 , Figure 2 As shown,

[0050] For any coherent state , a more practical loop-assisted quantum state amplifier design method includes the following steps:

[0051] Step 1: Add thermal noise to cause random displacement transformation of the coherent state and obtain the output state; the average number of photons of thermal noise is expressed as According to the Glauber-Sudarshan representation, the coherent state with thermal noise added The density matrix can be expressed as:

[0052]

[0053] in, is the amplitude of the input coherent state, is the integration variable, is the number of thermal noise photons, is a complex variable Elements of the double integral in the complex plane.

[0054] Step 2: Vacuum The output state of step 1 is coupled at the beam splitter to perform single-photon subtraction; The detection efficiency is The APD performs single-photon subtraction;

[0055] Step 3: Use a single photon detector to detect photons at the beam splitter coupling point. If the photons are successfully detected, the quantum state of the amplified output is directly obtained; otherwise, execute step 4; if the APD detects the photons, the operation is successful and the amplified quantum state is directly obtained; if the APD detection fails, go to step 3;

[0056] The projection operator that fails to detect is denoted as , the projection operator that successfully detects is recorded as ; APD indicates that after the photon subtraction is successful, the density matrix of the output state becomes:

[0057]

[0058] in, , is the transmittance of the beam splitter,

[0059] The predicted success probability is .

[0060] Step 4: Determine whether the number of cycles is greater than the maximum preset value. If not, re-enter the quantum state after the detection failure into the loop, perform photon subtraction, and return to step 3; otherwise, discard the quantum state.

[0061] The efficiency is The quantum optical switch will re-enter the loop after the detection failure and perform photon subtraction. After the APD detection fails, the quantum optical switch will continue to enter the loop until the detection is successful. In order to prevent the occurrence of an infinite loop, the maximum number of loops is limited to , when detected If it fails again, the quantum state is discarded;

[0062] The inefficient quantum optical switch can be modeled as an ideal optical switch and a transmittance The beam splitter has ; At this time, affected by the optical switch, the transmittance of the beam splitter in the scheme is equivalent to , the detector efficiency is equivalent to ;No. When the detection of the first cycle is successful, the success probability is , the density matrix of the quantum state is:

[0063]

[0064] After averaging all the possible numbers of successful detection loops, the success probability is , the density matrix of the final state is obtained as:

[0065] .

[0066] In order to further verify the effect of the design scheme, the scheme is analyzed through specific data as follows:

[0067] Probability of success The expressions for different cases have been given in the previous section. Since the density matrix of the final output state is and The other properties are calculated by Further calculation yields is the basis of all analysis. For the sake of simplicity, we assume that the coupling of the beam splitter is very weak and there are only 0 or 1 photons in the detector. In this case, the detector projection operator becomes , . The Wigner function in phase space The value at the point It can reflect the decoherence process of the coherent state to a certain extent. In order to obtain more decoherence information, the change of fidelity is also used as one of the analysis indicators of decoherence.

[0068]

[0069] .

[0070] Considering the feasibility of actual implementation, given , , , , the phase of the coherent state When the number of thermal noise photons is At different maximum number of cycles Under the value of , the performance of the solution changes as follows Figure 1 shown. Figure 1 The solid line “o” in (b) corresponds to , the “x” dashed line corresponds to the fidelity . It can be found that with The increase of , as well as There is a clear upward trend. This shows that for the quantum amplifier with thermal noise plus photon subtraction, adding a loop to the photon subtraction part can effectively improve the success probability of the scheme and reduce the decoherence in the quantum state transmission process.

[0071] Returning to the basic purpose of the quantum amplifier proposed by Marek et al., it is to measure the phase more accurately and reduce its phase uncertainty by amplifying the coherent state. For the coherent state, reducing the phase variance usually means lower phase uncertainty. By finding the relationship between the phase variance and the number of added thermal noise photons, the performance of the scheme can be further optimized. Here we use the standard phase variance To measure the phase uncertainty, the canonical measurement is used to estimate the phase of the quantum state, which is given by The calculation process of the expression is:

[0072]

[0073] in,

[0074]

[0075] .

[0076] exist When and The relationship is as Figure 2 As shown, with Changes There is a minimum value. The step size is 0.05, and when the step size is 0.01, the minimum , corresponding to the optimal The value of is 0.71.

[0077] Finally, consider the amplification gain Calculation:

[0078]

[0079] in is the average amplitude of the output state, .

[0080] Although setting up a loop in the quantum amplification scheme increases the success probability of the amplifier and reduces the decoherence of the quantum state, it is too large. This will increase the waiting time of the scheme, which is not conducive to its application in large-scale quantum communication. Therefore, in the further discussion of the scheme, we consider the maximum number of cycles. When the value is small, the performance of the scheme under different conditions is shown in Table 1. It should be noted that the bold values ​​in the thermal noise part of the table are the same as those in the adjacent rows to facilitate the analysis of the same The influence of changing other conditions on the performance is taken into account, and other thermal noise values ​​are all the optimal thermal noise that minimizes the standard phase variance in the corresponding situation.

[0081] Table 1 Performance of solutions in different situations

[0082]

[0083] Increase Regarding the success rate, And the significant improvement in fidelity has been achieved in the previous part Figure 1 An explanation is given. Based on the detector efficiency , optical switch efficiency In the case of , when the loop is not set to a maximum of 1 cycle, the amplification gain has decreased significantly, but it still has a good amplification effect for the coherent state. , amplification gain Decrease slowly; when When the value ranges from 1 to 5, It decreased from 2.9903 to 2.2880. This shows that increasing the number of loops in this scheme will not increase the success rate and reduce decoherence while eliminating the quantum amplification performance. The effects of the actual optical switch and detector are and When given: , When it changes from 1 to 0.9, the success rate decreases, but rise; when , When it changes from 1 to 0.8, the success rate increases, but When applied to practice, this result provides a possible optimization idea: when the application scheme focuses on improving the probability of success, it may be helpful to use the latest detection technology to achieve a more efficient APD; if the application focuses on better amplification under a reasonable probability of success, you can try to improve the optical switching technology to approach the ideal efficiency. Whether it is a real optical switch or a detector, the corresponding quantum probability amplification scheme requires a higher optimal thermal noise than the ideal situation. And when As increases, the required optimal thermal noise decreases.

[0084] based on , When , this scheme takes a smaller maximum number of cycles, that is, , corresponding to the optimal thermal noise of 0.72. When compared with the basic model without loop, the performance of this solution is improved as follows: the success rate is increased from 0.0367 to 0.1913, The fidelity increased from 0.7471 to 0.8074, and the success rate increased from 0.3749 to 0.4790. The quantum probability amplification scheme with loop design significantly improved the success probability and reduced the decoherence of the quantum state. Although the amplification gain decreased from 4.0271 to 2.2880, it still had a significant amplification effect.

[0085] The quantum state probability amplifier composed of thermal noise and photon subtraction can not only greatly amplify the coherent state, but also reduce its phase uncertainty to achieve the probability concentration of phase information. However, due to the existence of photon subtraction, the success probability of this scheme is usually very small. In order to improve the practicality and scalability of this measurement-induced amplification scheme, the present invention proposes a loop-assisted quantum amplifier scheme based on this quantum amplifier model, which not only significantly improves the success probability of the scheme, but also reduces the decoherence of the quantum state.

[0086] Even when the number of loops is very small (5), the success probability of this scheme is increased to 5.2 times the original one, and the decoherence of the quantum state is also reduced from This is reflected in the increase in resolution and fidelity, which are increased to 1.3 and 1.1 times the original respectively.

[0087] Those skilled in the art should understand that they can implement variations by combining the prior art and the above embodiments. Such variations do not affect the essence of the present solution and are not described in detail here.

[0088] It should be understood that the present solution is not limited to the above-mentioned specific implementation methods, and the devices and structures not described in detail should be understood to be implemented in a common manner in the art; any technician familiar with the art can use the above-disclosed methods and technical contents to make many possible changes and modifications to the technical solution of the present solution without departing from the scope of the technical solution of the present solution, or modify it into an equivalent embodiment with equivalent changes, which does not affect the essential content of the present solution. Therefore, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present solution without departing from the content of the technical solution of the present solution still falls within the scope of protection of the technical solution of the present solution.

Claims

1. A loop-assisted quantum state amplifier, characterized in that: It includes a quantum state amplification module and a photon subtraction module; the quantum state amplification module adds thermal noise to any input coherent state, resulting in random displacement transformation of the coherent state, and obtains a Gaussian mixed output state; the photon subtraction module includes a beam splitter, a single-photon detector, and a quantum optical switch at both ends of the beam splitter; the vacuum state and the output state of the quantum state amplification module are coupled at the beam splitter, and single-photon subtraction is performed. The single-photon detector is used to detect photons at the beam splitter. If photons are detected, the amplified quantum state is output; otherwise, the quantum optical switch transfers the quantum state into a loop and re-executes photon subtraction.

2. The loop-assisted quantum state amplifier according to claim 1, characterized in that: The loop has a preset maximum number of cycles.

3. The loop-assisted quantum state amplifier according to claim 2, characterized in that: The maximum number of cycles is determined according to the success probability and the amplification effect.

4. The loop-assisted quantum state amplifier according to claim 3, characterized in that: As the maximum number of cycles increases, the corresponding optimal thermal noise decreases.

5. A design method for a loop-assisted quantum state amplifier, characterized in that: The steps include: Step 1: Take any coherent state Add thermal noise, which causes random displacement transformation of the coherent state, and obtain the output state; Step 2: Vacuum Coupled with the output state of step 1 at the beam splitter to perform single-photon subtraction; Step 3: Use a single photon detector to detect photons at the beam splitter coupling point. If the photons are successfully detected, the quantum state of the amplified output is directly obtained; Otherwise, go to step 4; Step 4: Determine whether the number of cycles is greater than the maximum preset value. If not, re-enter the quantum state after the detection failure into the loop, perform photon subtraction, and return to step 3; otherwise, discard the quantum state.

6. The design method of the loop-assisted quantum state amplifier according to claim 5, characterized in that: A quantum optical switch is used to transfer the quantum state after detection failure back into the loop.

7. The design method of the loop-assisted quantum state amplifier according to claim 5, characterized in that: In step 1, the coherent state The density matrix after adding thermal noise is expressed as: ， in, , is the amplitude of the input coherent state, is the integration variable, is the number of thermal noise photons, is a complex variable Elements of the double integral in the complex plane.

8. The design method of the loop-assisted quantum state amplifier according to claim 7, characterized in that: After successful detection without loops, the density matrix of the output state becomes: ， in, , is the transmittance of the beam splitter, The predicted success probability is .

9. The design method of the loop-assisted quantum state amplifier according to claim 8, characterized in that: In step 4, When the next cycle detection is successful, the density matrix of the quantum state is: ， in, , The transmittance of the beam splitter obtained by equivalently modeling the inefficient optical switch, is the corresponding success probability.

10. The design method of the loop-assisted quantum state amplifier according to claim 9, characterized in that: After averaging all the possible numbers of successful detection loops, the success probability is , the density matrix of the final state is obtained as: 。

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