Photon detector chromatography method

Abstract

The invention provides a photon detector chromatography method, which comprises the following steps: acquiring a response range and a segment number of a target detector, dividing the response range into a plurality of sub-intervals according to the segment number, and obtaining an original boundary of the photon number of each sub-interval; obtaining the number of probes in each sub-interval, and generating a plurality of probes in the original boundary of the photon number of each sub-interval according to the number of the probes; according to the original boundary of the photon number of each sub-interval, constructing a Fokker distribution matrix of each sub-interval; for each subinterval, carrying out statistics on the conditional probability of response of the photon detector to the coherent light beam corresponding to each probe to obtain a conditional probability matrix of the subinterval; according to the Fokker distribution matrix and the conditional probability matrix of each subinterval, solving POVM elements of the subinterval; and recombining the POVM elements of all the subintervals to obtain a global POVM matrix.

Description

Technical Field

[0001] This invention relates to the field of quantum information technology, specifically to the field of quantum cryptography, and more specifically, to a photon detector tomography method. Background Technology

[0002] In the field of quantum detection, detector tomography is a core method for characterizing the quantum properties of photon detectors. It calibrates the detector itself as a black box, using light of known quantum states of various intensities as input, and inversely deduces the positive operator-valued measure (POVM) elements of the detector through the statistical results of the detector output, thereby fully characterizing the detector's response capability to arbitrary input light fields.

[0003] Existing standard protocols typically use coherent states as test probes: by preparing a series of coherent states with an average photon number (intensity) covering the entire response range of the detector, the conditional probabilities of the detector's output results under different input states are statistically analyzed. And based on the least squares optimization algorithm, the POVM elements are globally reconstructed. This represents the probability that the detector will produce a class j result when the average number of input photons is at the i-th intensity level. This method has been widely validated in single-photon detectors (such as avalanche photodiodes operating in Geiger mode) and small-scale photon number-resolved detectors (with response ranges typically below 100 photons). For example, tomographic schemes reported in existing literature, such as semiconductor single-photon detectors and superconducting nanowire single-photon detectors (SNSPDs), all rely on this global reconstruction framework, the mathematical essence of which is solving high-dimensional matrix equations. ,in, The conditional probability matrix, Let be the distribution matrix of the probe states under the Fock basis. Let be the matrix of POVM elements to be determined.

[0004] While traditional tomography methods perform well over a finite number of photons, they face fundamental limitations when dealing with wide dynamic range detectors such as linear-mode avalanche photodiodes (APDs). The core drawback lies in the complexity of least-squares reconstruction relative to the photon number range. and probe number The product exhibits a linear relationship, and the computational complexity increases catastrophically with the range of photon numbers. When the detector response range expands to thousands of photons, the dimension of the POVM matrix increases dramatically. Reconstructing at the thousand-photon level requires handling millions of matrix operations, resulting in enormous computational overhead for the global optimization problem, exceeding the real-time processing capabilities of conventional computing platforms.

[0005] It should be noted that the background information presented here is only for illustrating relevant information about the present invention to aid in understanding the technical solution of the present invention, and does not imply that the relevant information is necessarily prior art. The relevant information was submitted and disclosed together with the present invention, and should not be considered prior art unless there is evidence that the relevant information was disclosed before the filing date of the present invention. Summary of the Invention

[0006] Therefore, the purpose of this invention is to overcome the shortcomings of the prior art and provide a photon detector tomography method.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] According to a first aspect of the present invention, a photon detector tomography method is provided, comprising: obtaining the response range and number of segments of a target detector; dividing the response range into multiple sub-intervals according to the number of segments to obtain the original boundary of the photon number of each sub-interval; obtaining the number of probes in each sub-interval; generating multiple probes within the original boundary of the photon number of each sub-interval according to the number of probes; constructing a Fokker distribution matrix for each sub-interval according to the original boundary of the photon number of each sub-interval; for each sub-interval, calculating the conditional probability of the photon detector's response to the coherent beam corresponding to each probe to obtain the conditional probability matrix of that sub-interval; solving for the POVM elements of each sub-interval based on the Fokker distribution matrix and the conditional probability matrix of that sub-interval; and reorganizing the POVM elements of all sub-intervals to obtain a global POVM matrix. This scheme can achieve at least the following beneficial technical effects: the scheme divides the response range into multiple sub-intervals through a divide-and-conquer strategy, sets probes and performs statistics in each sub-interval, reconstructs the POVM elements of each photon number subspace, and then combines the POVM elements of each subspace POVM to obtain the global POVM matrix, which simplifies the computational complexity of reconstructing the global POVM matrix in the tomography process and significantly reduces the related computational overhead.

[0009] According to a second aspect of the present invention, a photon detector tomography method is provided, comprising: obtaining the response range and number of segments of a target detector; dividing the response range into multiple sub-intervals according to the number of segments to obtain the original boundary of the photon number of each sub-interval; obtaining the number of probes in each sub-interval; generating multiple probes within the original boundary of the photon number of each sub-interval according to the number of probes; extending the boundary based on the original boundary of the photon number of each sub-interval to obtain the extended photon number boundary of each sub-interval; constructing the extended Fokker distribution matrix of each sub-interval according to the extended photon number boundary of each sub-interval; for each sub-interval, calculating the conditional probability of the coherent beam response of the photon detector to each probe to obtain the conditional probability matrix of that sub-interval; solving for the extended POVM elements of that sub-interval according to the extended Fokker distribution matrix and the conditional probability matrix of each sub-interval; discarding the extended portion of the extended POVM elements of each sub-interval to obtain the POVM elements of each sub-interval; and recombining the POVM elements of all sub-intervals to obtain a global POVM matrix. This scheme achieves at least the following beneficial technical effects: It reconstructs the POVM elements of each photon number subspace separately using a divide-and-conquer strategy, and then combines the POVM elements of each subspace POVM, simplifying the algorithm complexity and experimental steps in the reconstruction process; In addition, the scheme first expands the original boundary of the photon number during the subspace tomography process, which is equivalent to expanding the computation window, and finally projects it back to the atomic space. Projecting back to the atomic space means discarding the expanded part (low-precision reconstruction results at the interval edges) in the expanded POVM submatrix, and only retaining the central high-confidence segment, thereby improving the accuracy of the POVM elements of each reconstructed sub-interval.

[0010] Optionally, the length of the sub-interval is the difference between the upper and lower bounds of the response range divided by the number of segments, where the number of segments is an integer greater than 1 and should be less than the upper limit of segments determined based on the upper and lower bounds of the response range. The upper limit of segments is:

[0011]

[0012] in, Indicates the upper bound of the response range. Indicates the lower bound of the response range. Represents the empirical coefficient. The value is set to 3.89. This scheme can achieve at least the following beneficial technical effects: the upper limit of the segmentation is determined based on the response range, avoiding setting too many segments entirely based on experience, which would result in the length of each sub-interval being too small, and preventing the ineffective use of some useful information from neighboring probes, thereby better ensuring the overall tomography effect.

[0013] Optionally, the extended photon number boundary for each sub-interval is obtained as follows:

[0014]

[0015]

[0016] in, Indicates the first The lower bound of the extended photon number boundary of each sub-interval, Indicates the first The upper bound of the extended photon number boundary of each sub-interval, Indicates the first The lower bound of the original boundary of each sub-interval. Set to 3.89, Indicates the first The upper bound of the original boundaries of each sub-interval. To find the maximum value function, This is the floor function. This is the floor function. This scheme can achieve at least the following beneficial technical effects: for different original boundaries, the original boundary can be personalized according to this scheme, theoretically reducing the Poisson distribution tail truncation error to less than... This better ensures the overall effectiveness of the partitioned chromatography.

[0017] Optionally, the extended Fok distribution matrix for each subinterval can be constructed as follows:

[0018]

[0019]

[0020] in, Indicates the first The Fok distribution matrix of each subinterval, Indicates the number of probes. for The elements in This indicates the number of photons observed. Indicates the first Each probe in the photon number basis The probability amplitude above, Indicates the first Average number of photons per probe This represents the base of the natural logarithm. This scheme achieves at least the following beneficial technical effects: it constructs an extended Fokker distribution matrix to assist in solving an extended POVM element (whose overall scale is larger than that of the POVM elements in its own subintervals, and the accuracy of the marginal results is relatively low), thereby extracting the POVM elements of each subinterval and better ensuring the accuracy of the tomographic results for each subinterval.

[0021] Optionally, the difference between the upper and lower bounds of the response range is greater than or equal to 1000. This scheme can achieve at least the following beneficial technical effects: it can perform tomography on photon detectors with a wider response range more quickly, and is preferably used for tomography on detectors with a difference between the upper and lower bounds of the response range greater than or equal to 1000.

[0022] Optionally, the photon detector is a photodetector, or the photon detector is a single-photon detector operating in linear mode.

[0023] According to a third aspect of the present invention, a method for testing a coherent beam is provided, comprising: performing multiple detections on the coherent beam to be evaluated using a photon detector, and statistically obtaining a conditional probability matrix; and estimating the parameters of the coherent beam to be evaluated based on the conditional probability matrix corresponding to the coherent beam to be evaluated and the global POVM matrix to be extracted from the photon detector according to the method described in the first or second aspect.

[0024] According to a fourth aspect of the present invention, an electronic device is provided, comprising: one or more processors; and a memory for storing executable instructions; wherein the one or more processors are configured to implement the steps of the method described in the first, second, or third aspect by executing the executable instructions. Attached Figure Description

[0025] The embodiments of the present invention will be further described below with reference to the accompanying drawings, wherein:

[0026] Figure 1 This is a schematic diagram of an optional implementation process of the photon detector tomography method according to an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of another optional implementation of the photon detector tomography method according to an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram of the tomography apparatus for a photon detector according to an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the invention.

[0030] As mentioned in the background section, although traditional tomography methods perform well within a finite photon number range, they face a fundamental bottleneck when dealing with wide dynamic range detectors. The core drawback is that the computational complexity increases catastrophically with the photon number range; reconstruction at the thousand-photon level requires handling millions of matrix operations, resulting in enormous computational overhead for global optimization problems. During their research on detector tomography, the inventors discovered that while single-photon detectors in linear mode are widely used, tomography work on them is still lacking. This is because when the response range of linear single-photon detectors is very large (thousands of photons), the computational load of the reconstruction process is enormous. Furthermore, the inventors found that when the response range is large, coherent light can only cover a small portion of the photon number range. That is, the photon number distribution (Poisson distribution) of the coherent state exhibits locality; the contribution of two probes that are far apart to each other's statistical results is negligible (the coefficient approaches zero after 3.89 standard deviations; for example, coherent light with an average photon number of 1000 has almost no effect on photon numbers above 2000). This reveals the key factors enabling the formulation of the method in this invention: the avalanche response exhibits statistical independence across different photon number intervals, and the POVM elements display block diagonal characteristics under Focke-Kiehl's rule. Based on this, the method employs a divide-and-conquer strategy to divide the response range into multiple sub-intervals. Within each sub-interval, probes are set up and statistics are performed to reconstruct the POVM elements for each photon number subspace. Then, the POVM elements from each subspace are combined to obtain the global POVM matrix. This simplifies the computational complexity of reconstructing the global POVM matrix during tomography and significantly reduces related computational overhead.

[0031] To facilitate understanding, the present invention will be illustrated below through specific implementation methods.

[0032] Implementation Method 1

[0033] According to one embodiment of the present invention, a photon detector tomography method is provided. This method uses a divide-and-conquer strategy to split the response range of a target detector into multiple sub-intervals, performs tomography within each sub-interval, reconstructs the POVM elements of each sub-interval, and then combines the POVM elements of each sub-interval to obtain the final global POVM matrix. This tomography method is preferably used for photon detectors with a wide response range; for example, it is preferably used for tomography of photon detectors whose difference between the upper and lower bounds of the response range is greater than or equal to a specified number (e.g., 1000, 1100, or 1500). Such a photon detector with a wide response range can be a single-photon detector operating in linear mode or a photodetector.

[0034] According to one embodiment of the present invention, a photon detector tomography method is provided, see [link to previous document]. Figure 1The process includes steps A1-A6. To better understand the present invention, each step will be described in detail below with reference to specific embodiments.

[0035] Step A1: Obtain the response range and number of segments of the target detector, divide the response range into multiple sub-intervals according to the number of segments, and obtain the original boundary of the photon number of each sub-interval.

[0036] According to one embodiment of the present invention, the response range of the target detector refers to the operating range within which the photon detector can detect the average number of photons after tomography. The response range is expressed as... Current tomographic methods all involve deploying probe resources globally within the response range, constructing the overall Fokker distribution matrix, and directly deriving the global POVM matrix. However, if the response range is wide (e.g., ...), ... This will lead to difficulties in solving the problem.

[0037] According to one embodiment of the present invention, the number of segments It can be specified by the implementer as needed, such as Alternatively, 20. Implementers can determine the optimal number of segments for a given response range based on experience or experimentation. Alternatively, implementers can determine the number of segments based on the length of each segment and the response range.

[0038] Considering that less experienced implementers might set too many segments, affecting the overall tomography effect, improvements can be made by providing alternative segment ranges. According to one embodiment of the invention, the length of the sub-interval is the difference between the upper and lower bounds of the response range divided by the number of segments, wherein the number of segments is an integer greater than 1 and should be less than the upper segment limit determined based on the upper and lower bounds of the response range. The upper segment limit is:

[0039]

[0040] in, Indicates the upper bound of the response range. Indicates the lower bound of the response range. Represents the empirical coefficient. Set to 3.89. This is equivalent to providing an alternative segment range [2, Within this segmentation range, the number of segments can be reasonably selected. This scheme can achieve at least the following beneficial technical effects: the upper limit of the segmentation is determined based on the response range, avoiding setting too many segments entirely based on experience, which would result in the length of each sub-interval being too small, preventing the ineffective use of some useful information from neighboring probes, thereby better ensuring the overall chromatography effect.

[0041] Within the set target photon number response range and determine the number of segments Then, the response range can be divided into multiple segments, each corresponding to a sub-interval, resulting in multiple sub-intervals. First, the length of each sub-interval corresponding to a segment is determined based on the response range and the number of segments. Then, for each sub-interval Calculate the original boundary of the current subinterval based on its length: , ,in, Indicates the first The lower bound of the original boundary of each sub-interval. Indicates the first The upper bound of the original boundaries of each sub-interval.

[0042] Step A2: Obtain the number of probes in each sub-interval, and generate multiple probes within the original boundary of the photon count in each sub-interval based on the number of probes.

[0043] According to one embodiment of the present invention, assuming the number of probes is... Then for each subinterval, generate Coherent state probes The original boundary is uniformly distributed in this sub-interval Inside, among them, Indicates the first A probe can be represented as:

[0044]

[0045] in, The base of the natural logarithm. Indicates the first Average number of photons per probe Represents a given complex amplitude Power of 1 Represents the number of photons Fock state (or photon number basis) ).

[0046] Assume the first probe starts from the lower bound of the original boundary. When deployment begins, the step size for deploying the probes is determined. By solving for each probe at this step size, the position of each probe can be obtained.

[0047] Step A3: Construct the Fok distribution matrix for each sub-interval based on the original boundaries of the photon number for each sub-interval.

[0048] According to one embodiment of the present invention, the Fok distribution matrix for each sub-interval is constructed as follows:

[0049]

[0050]

[0051] in, Indicates the first The Fok distribution matrix of each subinterval, Indicates the number of probes. for The elements in Indicates the number of photons observed. Indicates the first Each probe in the photon number basis The probability amplitude above, Indicates the first Average number of photons per probe It represents the base of the natural logarithm.

[0052] Step A4: For each sub-interval, calculate the conditional probability of the photon detector's response to the coherent beam corresponding to each probe, and obtain the conditional probability matrix for that sub-interval.

[0053] According to one embodiment of the present invention, this step involves tomographic data acquisition of the detector for each sub-interval to obtain the conditional probability matrix for each sub-interval. For example, for the sub-interval... , sub-interval of The coherent state beams corresponding to each probe are sequentially and repeatedly input into the photon detector, and the output signals are acquired by a high-speed ADC (i.e., high-speed analog-to-digital converter) (preferred sampling rate). 1GSPS), discretizing the analog signal into One of the output results is a class that calculates the conditional probability matrix for that sub-interval. ,in, , This indicates that when the input number is... The coherent beam corresponding to the probe (average photon number is the th) When the intensity is (level), the detector gives the first The probability of a class of results.

[0054] Step A5: Solve for the POVM elements of each subinterval based on the Fokker distribution matrix and conditional probability matrix.

[0055] According to one embodiment of the present invention, for sub-intervals Obtain the Fok distribution matrix for this subinterval. and conditional probability matrix Based on solving a constrained quadratic programming problem, the POVM elements for this subinterval are solved in the following manner:

[0056]

[0057] in, Describes the Frobenius norm. Subinterval The POVM matrix (containing this subinterval) (POVM elements) To smooth out the regularization weights (experimental values ​​ranged from 0.1 to 0.5), Indicates the first The POVM matrix of the th th th _ ... One diagonal element, Indicates the first The POVM matrix of the th th th _ ... One diagonal element.

[0058] Step A6: Concatenate the POVM elements of all sub-intervals to obtain the global POVM matrix.

[0059] According to one embodiment of the present invention, the global POVM matrix can first be initialized. Let be a zero matrix, where, Indicates the upper bound of the response range. Indicates the lower bound of the response range. This represents the total number of categories in the output results. Each sub-interval is calculated... POVM elements Then, update it to the corresponding position in the global POVM matrix: After the POVM elements of the last sub-interval are updated, the final reconstructed global POVM matrix is ​​obtained.

[0060] Implementation Method 2

[0061] The difference between this implementation method and implementation method 1 is that implementation method 1 does not expand the calculation window. In order to improve the accuracy of the POVM elements of each sub-interval, this embodiment expands the calculation window. Accordingly, the main difference is that steps B3, B4, B6 and B7 are different from those in implementation method 1.

[0062] According to one embodiment of the present invention, a photon detector tomography method is provided, see [link to previous document]. Figure 2 This includes steps B1-B8. To better understand the present invention, each step will be described in detail below with reference to specific embodiments.

[0063] Step B1: Obtain the response range and number of segments of the target detector, divide the response range into multiple sub-intervals according to the number of segments, and obtain the original boundary of the photon number of each sub-interval.

[0064] The implementation details of this step can be found in the details of step A1 mentioned above, and will not be repeated here.

[0065] Step B2: Obtain the number of probes in each sub-interval, and generate multiple probes within the original boundary of the photon count in each sub-interval based on the number of probes.

[0066] The implementation details of this step can be found in the details of step A2 mentioned above, and will not be repeated here.

[0067] Step B3: Extend the boundary based on the original boundary of the photon number of each sub-interval to obtain the extended photon number boundary of each sub-interval.

[0068] According to one embodiment of the present invention, the extended photon number boundary of each sub-interval is obtained as follows:

[0069]

[0070]

[0071] in, Indicates the first The lower bound of the extended photon number boundary of each sub-interval, Indicates the first The upper bound of the extended photon number boundary of each sub-interval, Indicates the first The lower bound of the original boundary of each sub-interval. Set to 3.89, Indicates the first The upper bound of the original boundaries of each sub-interval. To find the maximum value function, This is the floor function. This is the floor function. This scheme can achieve at least the following beneficial technical effects: For different original boundaries, the original boundaries can be personalized, which is equivalent to dynamically calculating the window expansion based on the original boundaries of each sub-interval, so that the information of some neighborhoods can be used in the derivation. Theoretically, this can reduce the Poisson distribution tail truncation error to less than [a certain value]. This better ensures the overall effectiveness of the partitioned chromatography.

[0072] Step B4: Construct the extended Fok distribution matrix for each sub-interval based on the extended photon number boundary of each sub-interval.

[0073] According to one embodiment of the present invention, the extended Fok distribution matrix for each sub-interval is constructed as follows:

[0074]

[0075]

[0076] in, Indicates the first The Fok distribution matrix with sub-interval expansion, Indicates the number of probes. for The elements in Indicates the number of photons observed. Indicates the first Each probe in the photon number basis The probability amplitude above, Indicates the first Average number of photons per probe This represents the base of the natural logarithm. Based on this extended Fokker distribution matrix, only its value in the photon number is considered. The amplitude within the subspace is negligible because, due to the expansion of the calculation window in step B3, the amplitude of the coherent probe within each subspace is almost zero outside that subspace. This scheme achieves at least the following beneficial technical effects: it constructs an extended Fokker distribution matrix to assist in solving an extended POVM element (whose overall scale is larger than that of the POVM elements in its own sub-intervals, and the accuracy of the edge results is relatively low), thereby extracting the POVM elements of each sub-interval and better ensuring the accuracy of the tomographic results for each sub-interval.

[0077] Step B5: For each sub-interval, calculate the conditional probability of the coherent beam response of the photon detector to each probe, and obtain the conditional probability matrix of that sub-interval.

[0078] The implementation details of this step can be found in step A4 above, and will not be repeated here.

[0079] Step B6: Solve for the extended POVM elements of each subinterval based on the extended Fokker distribution matrix and conditional probability matrix.

[0080] According to one embodiment of the present invention, for sub-intervals Obtain the extended Fokker distribution matrix for this sub-interval. and conditional probability matrix Based on solving the constrained quadratic programming problem, the extended POVM elements of this subinterval are solved in the following manner:

[0081]

[0082] in, Describes the Frobenius norm. Subinterval The extended POVM matrix (containing the sub-interval) (POVM elements) To smooth out the regularization weights (experimental values ​​ranged from 0.1 to 0.5), Indicates the first The POVM matrix of the th th th _ ... One diagonal element, Indicates the first The POVM matrix of the th th th _ ... One diagonal element.

[0083] Step B7: Discard the extended portion of the extended POVM element in each sub-interval to obtain the POVM element for each sub-interval.

[0084] According to one embodiment of the present invention, step B7 is mainly used for subspace projection and edge correction. For example: calculating the projection interval: Then from Extracting the high-confidence segment from the center yields each sub-interval. POVM elements: This means discarding the data at both ends of the extended window (the extended portion).

[0085] Step B8: Reorganize the POVM elements of all sub-intervals to obtain the global POVM matrix.

[0086] According to one embodiment of the present invention, the global POVM matrix can first be initialized. Let be a zero matrix, where, Indicates the upper bound of the response range. Indicates the lower bound of the response range. This represents the total number of categories in the output. Each sub-interval has a calculated POVM element. Then, update it to the corresponding position in the global POVM matrix: After the POVM elements of the last sub-interval are updated, the final reconstructed global POVM matrix is ​​obtained.

[0087] Implementation Method 3

[0088] See Figure 3 This embodiment provides an optional example of an apparatus for implementing the method of the present invention.

[0089] According to one embodiment of the present invention, a tomographic apparatus for a photon detector is provided, comprising:

[0090] The optical preparation system is configured to generate a laser beam by a continuous wave laser, and to change the intensity of the laser by an amplitude modulator AM and / or a variable optical attenuator VOA (either one or both can be used together) to obtain coherent states with different intensities. Then, the coherent states are split into two beams by a beam splitter. One beam is sent to an optical power meter, and the other beam is sent to a photon detector as the coherent state beam corresponding to the probe.

[0091] The detector tomography unit is configured to monitor the optical power via an optical power meter (PM) (in order to observe changes in optical power or whether the required requirements are met), adjust the operating state of the photon detector by setting the bias voltage (generally using the default voltage), amplify the current output of the photon detector through a transimpedance amplifier to obtain an amplified continuous signal, discretize the continuous signal through a high-speed ADC, and output the category result detected by the photon detector.

[0092] The post-processing system is configured to collect data and perform conditional probability statistics on the category results detected by the photon detector in each sub-interval, obtain the POVM elements of each sub-interval through segmented optimization calculation, and then perform POVM reconstruction to reorganize the POVM elements of all sub-intervals into a global POVM matrix.

[0093] In summary, some embodiments of the present invention can achieve at least one of the following beneficial effects:

[0094] (1) A new detector tomography method is provided, which is applicable to detectors with a wide response range (on the order of thousands of photons), such as single-photon detectors and photodetectors operating in linear mode. The method uses a divide-and-conquer strategy to analyze the full response range. Divide into T photon number sub-intervals, where the i-th sub-interval is... Each sub-interval is analyzed independently, reducing the algorithm's complexity and computational overhead in deriving the global POVM matrix. This scheme reduces computational complexity from O(TDM) to O(DM) with almost no loss of fidelity.

[0095] (2) Provide adaptive probe design: for sub-intervals D coherent states are generated, and the computation window is dynamically expanded to... Furthermore, by discarding the low-precision reconstruction results at the interval edges through subspace projection, only the high-confidence segments at the center are retained, edge errors are suppressed, and the Gaussian distribution (an approximation of the Poisson distribution under high expectation) tail is negligible, thus better ensuring the accuracy of the derived POVM elements of a single sub-interval.

[0096] (3) Through the three-dimensional synergy of physical characteristics (locality of coherent states), algorithm design (segmented optimization) and extended computation window to suppress edge errors, the long-standing gap in quantum characterization of wide dynamic range detectors was finally filled.

[0097] It should be noted that although the steps are described in a specific order above, it does not mean that the steps must be executed in the above specific order. In fact, some of these steps can be executed concurrently, or even in a different order, as long as the required function can be achieved.

[0098] This invention can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of the invention.

[0099] Computer-readable storage media can be tangible devices that hold and store instructions for use by an instruction execution device. Computer-readable storage media can include, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof.

[0100] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A photon detector tomography method, comprising: Obtain the response range and number of segments of the target detector, divide the response range into multiple sub-intervals according to the number of segments, and obtain the original boundary of the photon number of each sub-interval; Obtain the number of probes in each sub-interval, and generate multiple probes within the original boundary of the photon count in each sub-interval based on the number of probes. Construct the Fok distribution matrix for each sub-interval based on the original boundaries of the photon number for each sub-interval; For each sub-interval, the conditional probability of the photon detector's response to the coherent beam corresponding to each probe is statistically calculated to obtain the conditional probability matrix of that sub-interval. Based on the Fok distribution matrix and conditional probability matrix of each subinterval, solve for the POVM elements of that subinterval; Reorganize the POVM elements of all sub-intervals to obtain the global POVM matrix.

2. A photon detector tomography method, comprising: Obtain the response range and number of segments of the target detector, divide the response range into multiple sub-intervals according to the number of segments, and obtain the original boundary of the photon number of each sub-interval; Obtain the number of probes in each sub-interval, and generate multiple probes within the original boundary of the photon count in each sub-interval based on the number of probes. The boundary is extended based on the original boundary of the photon number of each sub-interval to obtain the extended photon number boundary of each sub-interval; Based on the extended photon number boundary of each sub-interval, construct the extended Fok distribution matrix for each sub-interval; For each sub-interval, the conditional probability of the coherent beam response of the photon detector to each probe is statistically calculated to obtain the conditional probability matrix of that sub-interval. Based on the extended Fokker distribution matrix and conditional probability matrix of each subinterval, solve for the extended POVM elements of that subinterval; Discard the extended portion of the extended POVM element in each sub-interval to obtain the POVM element for each sub-interval; Reorganize the POVM elements of all sub-intervals to obtain the global POVM matrix.

3. The method according to claim 1 or 2, characterized in that, The length of the subinterval is the difference between the upper and lower bounds of the response range divided by the number of segments, where the number of segments is an integer greater than 1 and should be less than the upper limit of segments determined by the upper and lower bounds of the response range. The upper limit of segments is: in, Indicates the upper bound of the response range. Indicates the lower bound of the response range. Represents the empirical coefficient. Set to 3.

89.

4. The method according to claim 2, characterized in that, The extended photon number boundary for each sub-interval is obtained as follows: in, Indicates the first The lower bound of the extended photon number boundary of each sub-interval, Indicates the first The upper bound of the extended photon number boundary of each sub-interval, Indicates the first The lower bound of the original boundary of each sub-interval. Set to 3.89, Indicates the first The upper bound of the original boundaries of each sub-interval. To find the maximum value function, This is the floor function. This is the floor function.

5. The method according to claim 4, characterized in that, Construct the extended Fok distribution matrix for each subinterval as follows: in, Indicates the first The Fok distribution matrix of each subinterval, Indicates the number of probes. for The elements in This indicates the number of photons observed. Indicates the first Each probe in the photon number basis The probability amplitude above, Indicates the first Average number of photons per probe It represents the base of the natural logarithm.

6. The method according to claim 1, 2, 4 or 5, characterized in that, The difference between the upper and lower bounds of the response range is greater than or equal to 1000.

7. The method according to claim 1, 2, 4 or 5, characterized in that, The photon detector is a photoelectric detector or a single-photon detector operating in linear mode.

8. A method for testing a coherent beam, comprising: The coherent beam to be evaluated is detected multiple times using a photon detector, and the conditional probability matrix is ​​obtained statistically. The parameters of the coherent beam to be evaluated are estimated based on the conditional probability matrix corresponding to the coherent beam to be evaluated and the global POVM matrix extracted from the photon detector by the method according to any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, It stores a computer program that can be executed by a processor to implement the steps of the method according to any one of claims 1-7.

10. An electronic device, characterized in that, include: One or more processors; as well as Memory, wherein the memory is used to store executable instructions; The one or more processors are configured to implement the steps of the method according to any one of claims 1-7 by executing the executable instructions.

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