An orbital angular momentum entanglement measurement method, system and device

Abstract

The application discloses a kind of orbital angular momentum entanglement measurement method, system and equipment, it is related to quantum state chromatography technical field.High-dimensional orbital angular momentum entangled state is acquired;The high-dimensional orbital angular momentum entangled state includes: signal photon and idler photon;Signal photon and idler photon one-to-one correspondence;Signal photon is projected on first superposition state and second superposition state in turn, simultaneously, with the idler photon corresponding to signal photon collapse, and get collapse state;According to the collapse state, two spatial mode images are obtained by ICCD camera;Two spatial mode images are input into quantum state chromatography model respectively for calculation, and the representation result of orbital angular momentum entanglement is obtained.The application improves the efficiency of orbital angular momentum entanglement measurement.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of quantum state tomography, in particular to an orbital angular momentum entanglement measurement method, system and device. BACKGROUND

[0002] Orbital angular momentum is an ideal resource for realizing high-dimensional entanglement due to its discrete and unbounded Hilbert space advantage. Such high-dimensional entanglement not only effectively increases the amount of information, but also resists more environmental noise. However, the detection and characterization of high-dimensional orbital angular momentum entanglement is still challenging.

[0003] Traditional quantum state tomography methods all need to select multiple different measurement basis vectors to perform a large number of projection measurements on unknown quantum states. In particular, as the dimension increases, the number of measurements increases geometrically, and the required calculation time also greatly increases, making the tomography of high-dimensional entangled states more and more cumbersome and difficult, and even an impossible task, which has the problem of low measurement efficiency. SUMMARY

[0004] The purpose of the embodiments of the present application is to provide an orbital angular momentum entanglement measurement method, system and device to improve the efficiency of orbital angular momentum entanglement measurement.

[0005] To achieve the above purpose, the embodiments of the present application provide the following solutions:

[0006] An orbital angular momentum entanglement measurement method, comprising:

[0007] Obtaining a high-dimensional orbital angular momentum entangled state; the high-dimensional orbital angular momentum entangled state comprising: a signal photon and an idler photon; the signal photon and the idler photon corresponding one by one;

[0008] Projecting the signal photon onto a first superposition state and a second superposition state in turn, while the idler photon corresponding to the signal photon collapses to obtain a collapsed state;

[0009] Obtaining two spatial mode images according to the collapsed state;

[0010] Inputting the two spatial mode images into a trained quantum state tomography model for calculation to obtain a characterization result of orbital angular momentum entanglement measurement.

[0011] Optionally, the high-dimensional orbital angular momentum entangled state is generated in a spontaneous parametric down-conversion process of a Gaussian beam pumping a nonlinear crystal, and specifically comprises:

[0012]

[0013] Wherein, |l> s| l > represents an orbital angular momentum state of a signal photon (s) generated in a spontaneous parametric down-conversion process, with quantum number l; | l > i | l > represents an orbital angular momentum state of an idler photon (i) generated in a spontaneous parametric down-conversion process, with quantum number l; | l > represents a Laguerre-Gaussian mode with topological charge l and radial index zero; α l ≥0 is a direct product state | l > s | -l > is a direct product state | l > i | -l > is a direct product state | l > l φ ∈ [0, 2π) is a phase of the direct product state | l > s | -l > is a direct product state | l > i | -l > is a direct product state | l > | l > represents a probability that the signal photon is in | l > s | -l > represents a probability that the idler photon is in | -l > i | -l > represents a probability that the signal photon is in | l >

[0014] Optionally, the signal photon is sequentially projected onto the first superposition state and the second superposition state, specifically comprising:

[0015] Two holographic gratings on a spatial light modulator are used to obtain the first superposition state and the second superposition state; the specific formula is:

[0016]

[0017]

[0018] The signal photon is sequentially projected onto the first superposition state | l > M and the second superposition state | -l > K for measurement; wherein M l represents a normalized complex coefficient of the first superposition state, and K l represents a normalized complex coefficient of the second superposition state.

[0019] Optionally, two spatial mode images are obtained according to the collapsed state, specifically comprising:

[0020] An ICCD camera is used to sequentially record the collapsed state of the idler photon to obtain a first spatial mode image and a second spatial mode image; the calculation formula is as follows:

[0021]

[0022]

[0023]

[0024] wherein, represents the first spatial mode image, represents the second spatial mode image, and αl φ represents all amplitude information of the entangled state to be measured. l It represents all phase information of the entangled state to be tested; the superscript * indicates complex conjugation.

[0025] Optionally, the quantum state tomography model specifically includes: an input layer, a convolutional module, a fully connected layer, and an output layer.

[0026] Optionally, the convolution module includes M convolutional units.

[0027] Optionally, any one of the convolutional units includes: a convolutional layer, a batch normalization layer, a non-linear activation function, and a max pooling layer.

[0028] To achieve the above objectives, embodiments of the present invention also provide the following solutions:

[0029] An orbital angular momentum entanglement measurement system includes:

[0030] An orbital angular momentum entangled state acquisition module is used to acquire high-dimensional orbital angular momentum entangled states; the high-dimensional orbital angular momentum entangled states include: signal photons and idler photons; the signal photons and idler photons correspond one-to-one;

[0031] The projection and collapse module is connected to the orbital angular momentum entangled state acquisition module. It is used to project the signal photon onto the first superposition state and the second superposition state in sequence. At the same time, the idler photon corresponding to the signal photon collapses to obtain the collapsed state.

[0032] An imaging module, connected to the projection and collapse module, is used to obtain two spatial pattern images based on the collapse state.

[0033] The output module, connected to the imaging module, is used to input the two spatial pattern images into the trained quantum state tomography model for calculation, and obtain the characterization results of the orbital angular momentum entanglement measurement.

[0034] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the orbital angular momentum entanglement measurement method.

[0035] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed, implements the orbital angular momentum entanglement measurement method.

[0036] In this embodiment of the invention, applying the quantum state tomography model to orbital angular momentum entanglement measurement can greatly reduce computational complexity and time cost, and improve the efficiency of orbital angular momentum entanglement measurement. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a schematic flowchart of the orbital angular momentum entanglement measurement method provided in an embodiment of the present invention;

[0039] Figure 2 A detailed structural diagram of the orbital angular momentum entanglement measurement system provided in an embodiment of the present invention;

[0040] Figure 3 A detailed schematic diagram of the orbital angular momentum entanglement measurement method provided in an embodiment of the present invention;

[0041] Figure 4 This is a schematic diagram of the quantum state tomography model structure provided in an embodiment of the present invention.

[0042] Symbol explanation:

[0043] Module for acquiring entangled states with orbital angular momentum -1, Module for projection and collapse -2, Module for imaging -3, Module for output -4, Signal photon -5, Idle photon -6, Holographic grating -8, First spatial mode image -9, Second spatial mode image -10, Spatial light modulator -11, ICCD camera -12, Quantum state tomography model -13, Input layer -14, Convolution module -15, Fully connected layer -16, Output layer -17, Convolution unit -18, Convolutional layer -19, Batch normalization layer -20, Nonlinear activation function -21, Max pooling layer -22. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] The purpose of this invention is to provide a method, system, and device for measuring orbital angular momentum entanglement, so as to solve the problem of low efficiency in existing orbital angular momentum entanglement measurements.

[0046] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] High-dimensional orbital angular momentum entanglement can not only effectively improve quantum channel capacity, but also effectively resist environmental noise. Since the number of measurements in traditional quantum state tomography increases exponentially with the increase of dimensionality, the characterization of high-dimensional entangled states becomes time-consuming and cumbersome. Therefore, how to efficiently characterize high-dimensional quantum entangled states has become a challenge.

[0048] Here, convolutional neural networks are applied to photonic orbital angular momentum quantum state tomography, which requires only two projection measurements to effectively reconstruct the density matrix of high-dimensional orbital angular momentum entangled states. This method can also be applied to complex cases involving mixed entangled states and tomographic measurements with noise or incomplete reception. Applying convolutional neural networks to quantum state tomography can significantly reduce computational complexity and time costs, and improve the efficiency of characterizing orbital angular momentum entangled states.

[0049] Figure 1 An exemplary procedure for measuring the orbital angular momentum entanglement described above is shown. The steps are described in detail below.

[0050] Step 1: Obtain a high-dimensional orbital angular momentum entangled state; the high-dimensional orbital angular momentum entangled state includes: signal photon 5 and idler photon 6; the signal photon 5 and idler photon 6 correspond one-to-one;

[0051] The high-dimensional orbital angular momentum entangled state is generated during the spontaneous parametric downconversion process of a Gaussian beam-pumped nonlinear crystal, specifically including:

[0052]

[0053] Among them, |l> s This represents the orbital angular momentum state of the signal photon (s) with quantum number l generated during the spontaneous parametric downconversion process; |l> i α represents the orbital angular momentum state of an idler photon (i) with quantum number l generated during spontaneous parametric downconversion; |l> represents a Laguerre-Gaussian mode with topological charge l and radial exponent zero; l ≥0 represents a direct product state |l> s |-l> i The amplitude; φ l ∈[0,2π) is a direct product state |l> s |-l> i The phase, and satisfies the normalization condition. This indicates that the signal photon is in |l> s Meanwhile, the idle frequency photon is in the |-l> i The probability of.

[0054] In one example, the generated signal photon 5 (Signal) and idler photon 6 (Idler) are as follows: Figure 3 As shown.

[0055] Step 2: Project the signal photon 5 onto the first superposition state and the second superposition state in sequence. At the same time, the idler photon 6 corresponding to the signal photon 5 collapses to obtain a collapsed state.

[0056] Projecting the signal photon 5 sequentially onto the first superposition state and the second superposition state specifically includes:

[0057] Using two holographic gratings on the spatial light modulator 11, the first superposition state and the second superposition state are obtained; the specific formula is as follows:

[0058]

[0059]

[0060] The signal photon 5 is sequentially projected onto the first superposition state. Second superposition state Measurements were taken on the surface; where M... l K represents the normalized complex coefficients of the first superposition state. l This represents the normalized complex coefficient of the second superposition state.

[0061] Step 3: Based on the collapsed state, obtain two spatial pattern images; specifically including:

[0062] The collapse state of the idler photon 6 is recorded sequentially using an ICCD camera 12 to obtain a first spatial mode image 9 and a second spatial mode image 10; the calculation formula is as follows:

[0063]

[0064]

[0065]

[0066] in, Image 9 represents the first spatial pattern. Image 10, representing the second spatial pattern. l φ represents all amplitude information of the entangled state to be measured. l It represents all phase information of the entangled state to be tested; the superscript * indicates complex conjugation.

[0067] Step 4: Input the two spatial pattern images into the quantum state tomography model 13 for measurement to obtain the orbital angular momentum entanglement measurement results.

[0068] The quantum state tomography model 13 specifically includes: an input layer 14, a convolutional module 15, a fully connected layer 16, and an output layer 17.

[0069] The convolution module 15 includes M convolution units 18.

[0070] Each of the convolutional units 18 includes: a convolutional layer 19, a batch normalization layer 20, a non-linear activation function 21, and a max pooling layer 22.

[0071] In one example, see Figure 4 The intensity distribution pattern of idler photon 6 with a size of 301*301 (first spatial mode image 9 and second spatial mode image 10) is input into the input layer 14 of quantum state tomography model 13.

[0072] The convolutional module 15 includes a convolutional layer 19, a batch normalization layer 20, a non-linear activation function 21, and a max pooling layer 22.

[0073] The quantum state tomography model 13 has four convolutional modules 15, with 8 (301*301), 16 (150*150), 32 (75*75), and 64 (37*37) convolutional units 18 respectively. Of course, those skilled in the art can also flexibly design the value of M, such as 4, 5, 6, etc., which will not be elaborated here. The following text takes 4 as an example.

[0074] The kernel size of convolution unit 18 is set to 3×3, and the stride is (1,1). Convolution operations are performed sequentially on different positions of the input intensity distribution pattern.

[0075] Each convolutional unit 18 has a batch normalization layer 20 to avoid overfitting and improve training efficiency.

[0076] The nonlinear activation function 21 can specifically be the ReLU function, which improves the nonlinear description capability of the quantum state tomography model 13.

[0077] A max-pooling layer 22 with a kernel size of 2×2 and a stride of (2,2) is used to filter out the information extracted from the previous layer. Finally, the feature information is passed to a fully connected layer 16. Unlike the classification task, a regression output function is used in the output layer 17 to judge the recognition pattern and give the predicted value.

[0078] The training process of quantum state tomography model 13 is described in detail below.

[0079] Example 1:

[0080] Taking the three-dimensional orbital angular momentum entangled state of two photons (signal photon 5 and idler photon 6) as an example, by using the first superposition state Second superposition state As the projection basis vector of signal photon 5, two corresponding patterns (first spatial mode image 9 and second spatial mode image 10) of idler photon 6 can be obtained by ICCD camera 12, which is determined by the entanglement parameters:

[0081]

[0082]

[0083] To improve calculation speed, the above formula is rewritten as:

[0084]

[0085]

[0086] Where 0≤θ1,θ2≤π / 2, then the first spatial pattern image 9 is labeled with {θ1,φ1}, {θ2,φ -1 Image 10 is labeled with the second spatial pattern. Two sets of training and test sets are generated by changing the values ​​of θ and φ. In the training set, phases φ1 and φ2 are... -1 From 0 to 2π, Δφ = 0.05; from θ1 and θ2 to π / 2, Δθ = 0.05. In the test set, phases φ1 and φ... -1 From 0 to 2π, Δφ = 0.07; θ1 and θ2 from 0 to π / 2, Δθ = 0.07. Two quantum state tomography models 13 (Net3-1 and Net3-2) are trained using the first spatial pattern image 9 and the second spatial pattern image 10 obtained from the simulation, respectively.

[0087] Figure 4 Using Net3-1 as an example, the parameter settings for the two quantum state tomography models 13 are identical. The weight parameters of quantum state tomography model 13 were trained using the Adam optimizer for 70 epochs with a batch size of 256. The initial learning rate was set to 0.0001, decreasing by a factor of 10 every 20 epochs. A dropout layer of size 0.008 was set to prevent overfitting. The training process was performed using MATLAB software.

[0088] The trained quantum state tomography model 13 can be used to predict the intensity pattern of the idler photon 6 after two projection measurements obtained from experiments or simulations, and obtain the predicted values ​​{θ, φ}. The corresponding amplitude α can then be calculated. l and phase φ l The value can be used to measure the entanglement of orbital angular momentum.

[0089] Please see Figure 3A high-dimensional orbital angular momentum entangled state is generated through a spontaneous parametric downconversion process. The generated signal photon 5 is projected onto a holographic grating via a spatial light modulator (SLM) for measurement. Simultaneously, the ICCD camera 12 is triggered, causing it to record only the spatial pattern of the idler photon 6 associated with the signal photon 5, and input into the quantum state tomography model 13 to retrieve the entanglement parameters. The two measurement images received by the ICCD camera 12 are sampled at a resolution of 301×301 pixels and processed as input to the quantum state tomography model 13, realizing the tomographic measurement of arbitrary-dimensional orbital angular momentum entangled states.

[0090] In summary, in the embodiments of the present invention, applying the quantum state tomography model to orbital angular momentum entanglement measurement can greatly reduce computational complexity and time cost, and improve the efficiency of orbital angular momentum entanglement measurement.

[0091] To achieve the above objectives, embodiments of the present invention also provide the following solutions:

[0092] Please refer to the following: An orbital angular momentum entanglement measurement system. Figure 2 ,include:

[0093] The orbital angular momentum entangled state acquisition module 1 is used to acquire high-dimensional orbital angular momentum entangled states; the high-dimensional orbital angular momentum entangled states include: signal photons and idler photons; the signal photons and idler photons correspond one-to-one;

[0094] The projection and collapse module 2 is connected to the orbital angular momentum entangled state acquisition module 1. The projection and collapse module 2 is used to project the signal photon onto the first superposition state and the second superposition state in sequence. At the same time, the idler photon corresponding to the signal photon collapses to obtain the collapsed state.

[0095] The imaging module 3 is connected to the projection and collapse module 2. The imaging module 3 is used to obtain two spatial pattern images according to the collapse state.

[0096] The output module 4 is connected to the imaging module 3. The output module 4 is used to input the two spatial pattern images into the trained quantum state tomography model for calculation to obtain the characterization results of orbital angular momentum entanglement measurement.

[0097] Furthermore, the present invention also provides an electronic device, which may include: a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor can call a computer program stored in the memory to execute the aforementioned orbital angular momentum entanglement measurement method.

[0098] Furthermore, when the computer program in the aforementioned memory is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0099] Furthermore, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the orbital angular momentum entanglement measurement method.

[0100] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0101] This document uses specific examples to illustrate the principles and implementation methods of the embodiments of the present invention. The descriptions of the embodiments above are only for the purpose of helping to understand the methods and core ideas of the embodiments of the present invention. At the same time, for those skilled in the art, there will be changes in specific implementation methods and application scope based on the ideas of the embodiments of the present invention. In summary, the content of this specification should not be construed as a limitation on the embodiments of the present invention.

Claims

1. A method for measuring orbital angular momentum entanglement, characterized in that, include: Obtaining high-dimensional orbital angular momentum entangled states; The high-dimensional orbital angular momentum entangled state includes: a signal photon and an idler photon; the signal photon and the idler photon correspond one-to-one. The signal photon is sequentially projected onto a first superposition state and a second superposition state. Simultaneously, the idler photon corresponding to the signal photon collapses to obtain a collapsed state. Specifically, projecting the signal photon sequentially onto the first superposition state and the second superposition state involves using two holographic gratings on a spatial light modulator to obtain the first superposition state and the second superposition state. The specific formula is as follows: The signal photons are sequentially projected onto the first superposition state. Second superposition state Measurements were taken on the surface; where M... l K represents the normalized complex coefficients of the first superposition state. l Represents the normalized complex coefficients of the second superposition state; Based on the collapsed state, two spatial pattern images are obtained, specifically including: The collapse states of the idler photons are recorded sequentially using an ICCD camera to obtain a first spatial mode image and a second spatial mode image; the calculation formula is as follows: in, Represents the first spatial pattern image. Represents the second spatial pattern image, α l Represents all amplitude information of the entangled state to be measured, Ф l This represents all phase information of the entangled state to be tested; the superscript * indicates complex conjugation; The two spatial pattern images are input into the trained quantum state tomography model for calculation, and the characterization results of orbital angular momentum entanglement measurement are obtained.

2. The method for measuring orbital angular momentum entanglement according to claim 1, characterized in that, The high-dimensional orbital angular momentum entangled state is generated during the spontaneous parametric downconversion process of a Gaussian beam-pumped nonlinear crystal, specifically including: Among them, |l> s This represents the orbital angular momentum state of the signal photon (s) with quantum number l generated during the spontaneous parametric downconversion process; |l> i α represents the orbital angular momentum state of an idler photon (i) with quantum number l generated during spontaneous parametric downconversion; |l> represents a Laguerre-Gaussian mode with topological charge l and radial exponent zero; l ≥0 represents a direct product state |l> s |-l> i The amplitude; Ф1∈[0,2π) is the product state |l> s |-l> i The phase, and satisfies the normalization condition. This indicates that the signal photon is in |l> s Meanwhile, the idle frequency photon is in the |-l> i The probability of.

3. The method for measuring orbital angular momentum entanglement according to claim 1, characterized in that, The quantum state tomography model specifically includes: an input layer, a convolutional module, a fully connected layer, and an output layer.

4. The method for measuring orbital angular momentum entanglement according to claim 3, characterized in that, The convolution module includes M convolutional units.

5. The method for measuring orbital angular momentum entanglement according to claim 4, characterized in that, Each of the convolutional units includes: a convolutional layer, a batch normalization layer, a non-linear activation function, and a max pooling layer.

6. A system for measuring orbital angular momentum entanglement, characterized in that, include: The orbital angular momentum entangled state acquisition module is used to acquire high-dimensional orbital angular momentum entangled states; The high-dimensional orbital angular momentum entangled state includes: a signal photon and an idler photon; the signal photon and the idler photon correspond one-to-one. The projection and collapse module is connected to the orbital angular momentum entangled state acquisition module. It is used to project the signal photon onto the first superposition state and the second superposition state in sequence. At the same time, the idler photon corresponding to the signal photon collapses to obtain the collapsed state. Projecting the signal photons sequentially onto the first superposition state and the second superposition state specifically includes: Using two holographic gratings on a spatial light modulator, the first superposition state and the second superposition state are obtained; the specific formula is as follows: The signal photons are sequentially projected onto the first superposition state. Second superposition state Measurements were taken on the surface; where M... l K represents the normalized complex coefficients of the first superposition state. l Represents the normalized complex coefficients of the second superposition state An imaging module, connected to the projection and collapse module, is used to obtain two spatial pattern images based on the collapse state, specifically including: The collapse states of the idler photons are recorded sequentially using an ICCD camera to obtain a first spatial mode image and a second spatial mode image; the calculation formula is as follows: in, Represents the first spatial pattern image. Represents the second spatial pattern image, α l Represents all amplitude information of the entangled state to be measured, Ф l This represents all phase information of the entangled state to be tested; the superscript * indicates complex conjugation; The output module, connected to the imaging module, is used to input the two spatial pattern images into the trained quantum state tomography model for calculation, and obtain the characterization results of the orbital angular momentum entanglement measurement.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the orbital angular momentum entanglement measurement method as described in claims 1-5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the orbital angular momentum entanglement measurement method as described in claims 1-5.

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