Collinear Entanglement Teaching Experiment Box, System, and Operation Method Based on BS Spectroscopy Technology

Abstract

This invention relates to the field of quantum information science, and provides a collinear entanglement teaching experiment box, system, and operation method based on BS beam splitting technology. The experiment box includes: an electronic control system installed in the lower box, and a quantum light source system, a walk-off compensation system, and a polarization state detection system arranged sequentially along the optical path in the upper box; the quantum light source system includes a laser, a focusing lens, and a polarization beam splitter arranged sequentially along the optical path; after being split by the polarization beam splitter, one beam enters the optical waste bin, and the other beam passes sequentially through a barium borate crystal and the beam splitter; the walk-off compensation system includes two identical optical paths, each including a half-wave plate, a secondary BBO crystal, and a mirror arranged sequentially; the polarization state detection system includes two identical optical paths, each including a polarizer, a filter, and an fiber coupler arranged sequentially; the electronic control system includes a first single-photon detector, a second single-photon detector, and a coincidence counter.

Description

Technical Field

[0001] This invention relates to the field of quantum information science, and in particular to a collinear entanglement teaching experiment box, system and operation method based on BS spectral splitting technology. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Quantum entanglement, a peculiar correlation phenomenon existing in two- or many-body quantum systems, is characterized by its nonlocality, which is its most fundamental feature at the microscopic scale. Therefore, introducing quantum entanglement experiments into the classroom, allowing students to conduct hands-on experiments to deepen their understanding of this phenomenon, is particularly important.

[0004] Currently, undergraduate education in quantum information science is in its initial stage. Few universities conduct quantum information-related experiments in undergraduate physics lab teaching. Students' understanding of it is mainly based on abstract theoretical learning, which is quite difficult to comprehend. The teaching of quantum entanglement experiments is immature and lacks corresponding professional equipment. Existing quantum entanglement experimental devices have several problems in teaching.

[0005] First, these devices are complex and expensive, requiring highly specialized optical platforms, making them difficult for students to understand and operate. Second, the experiments require specific environments, such as low temperatures and low noise, increasing the difficulty and cost. Furthermore, students must possess advanced technical knowledge and skills to operate these devices, and adjusting the experimental optical paths is extremely cumbersome, leading to slow progress. Most importantly, due to the aforementioned problems, only a small number of students can participate in the experiments, limiting the scope of participation. In conclusion, existing quantum entanglement experimental devices have several shortcomings in teaching, affecting students' learning experience and experimental progress. Summary of the Invention

[0006] To address the technical problems of traditional optical quantum entanglement experiments, which often require specialized optical platforms, are complex, costly, have low integration, and are subject to strict environmental requirements, complex optical path adjustments, and result in excessively long adjustment times and low success rates for students, this invention provides a collinear entanglement teaching experiment box, system, and operating method based on BS beam splitting technology. The invention features a simple optical path design with fewer components, and the quantum light source and pump light source are collinear, significantly reducing the difficulty of adjusting the optical path. Furthermore, it integrates the traditional optical quantum entanglement system into a single instrument. After the optical path is adjusted, it is fixed inside the instrument, eliminating the need for complex optical path adjustments during the experiment. Students only need to rotate the analyzer to observe the experimental phenomena, allowing them to focus more on the preparation and measurement of entanglement itself. The laser is placed inside the housing, avoiding exposure of the high-power laser and greatly improving the safety of the experiment.

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

[0008] The first aspect of the present invention provides a collinear entanglement teaching experiment box based on BS spectral splitting technology.

[0009] The collinear entanglement teaching experiment box based on BS beam splitting technology includes a lower box and an upper box. The lower box contains an electronic control system, and the upper box contains a quantum light source system, a walk-off compensation system, and a polarization state detection system arranged sequentially along the optical path. The electronic control system is connected to the polarization state detection system via optical fiber.

[0010] The quantum light source system includes a laser, a focusing lens, and a polarization beam splitter arranged sequentially along the optical path. After being split by the polarization beam splitter, one beam of light enters the optical trash can, and the other beam passes sequentially through a barium borate crystal and the beam splitter.

[0011] The walk-off compensation system includes two identical optical paths, each of which includes a half-wave plate, a secondary BBO crystal, and a reflector arranged sequentially.

[0012] The polarization state detection system includes two identical optical paths, each of which includes a polarizer, a filter, and an optical fiber coupler arranged sequentially.

[0013] The electronic control system includes a first single-photon detector, a second single-photon detector, and a coincidence counter, wherein both the first and second single-photon detectors are connected to the coincidence counter.

[0014] Furthermore, the laser is used to generate continuous pump light with a wavelength of 405 nm and a vertical polarization state;

[0015] Furthermore, the polarization beam splitter is used to separate the |H> light and |V> light in the light source;

[0016] Furthermore, the optical trash can is used to collect |H> light;

[0017] Furthermore, the barium metaborate crystal is used to convert a photon with polarization state |V> into two correlated photon pairs with polarization states |H> and |V> respectively;

[0018] Furthermore, the beam splitter is used to split the |H>|V> light into two paths; one path is the |H> light and the other path is the |V> light.

[0019] Furthermore, the walk-off compensation system is used to compensate for the temporal and spatial walk-off of light when it passes through the barium borate crystal.

[0020] Furthermore, both of the aforementioned mirrors are positioned at 45° to maintain the horizontal and vertical alignment of the light path.

[0021] Furthermore, the polarization state detection system is used to examine the polarization state of photons by rotating the polarizer to different angles, and is used to verify the CHSH inequality.

[0022] Furthermore, the experimental box is equipped with a power switch, a power input port, and a data transmission port. The power switch is used to control the on / off state of the laser, the first single-photon detector, the second single-photon detector, and the coincidence counting control device.

[0023] A second aspect of the present invention provides a collinear entanglement teaching system based on BS spectral splitting technology.

[0024] A collinear entanglement teaching system based on BS spectral splitting technology includes a collinear entanglement teaching experimental box based on BS spectral splitting technology as described in the first aspect and a host computer, wherein the host computer is connected to an electronic control system.

[0025] Furthermore, the host computer includes:

[0026] The quantum entanglement experiment principle demonstration module is used to demonstrate the experimental principle of quantum entanglement and the operation process of the collinear entanglement teaching experiment box;

[0027] The real-time experimental data display module is used to display experimental data during the collinear entanglement teaching experiment.

[0028] The historical experiment record display module is used to display the experimental records of historical collinear entanglement teaching experiments.

[0029] A third aspect of the present invention provides a collinear entanglement teaching operation method based on BS spectral splitting technology.

[0030] A collinear entanglement teaching method based on BS spectral splitting technology, employing the collinear entanglement teaching system based on BS spectral splitting technology described in the second aspect, includes:

[0031] Adjust all components to their initial state, and connect the power supply to both the collinear entanglement teaching experiment box and the host computer.

[0032] Remove the polarization beam splitter, the laser emits laser light, and the initial coincidence count value of the coincidence counter is recorded;

[0033] A polarization beam splitter is installed, and the laser emits laser light. The polarization state of the photons is checked by rotating the polarizer to different angles, which is used to verify the CHSH inequality.

[0034] Record the number of photons received by the first and second single-photon detectors, as well as the coincidence count.

[0035] Furthermore, the process of verifying the CHSH inequality by rotating the polarizer to different angles to check the polarization state of photons includes:

[0036] Under the basis vectors |H> and |V>, Alice & Bob has a minimum value when the angles of the two polarizers are both 0° or both are 90°, and a maximum value when the angles of the two polarizers are 0° and 90° and 90° and 0° respectively, and the ratio of the maximum value to the minimum value is greater than 15:1.

[0037] Under the |+> and |-> basis vectors, Alice & Bob has a maximum value when the angles of the two polarizers are both 45°, and a minimum value when the angles of the two polarizers are 45° and 135° and 135° and 45° respectively, and the ratio of the maximum value to the minimum value is greater than 7:1; so as to perform CHSH inequality measurement.

[0038] Alice & Bob represent the number of photons arriving at both single-photon detectors simultaneously per second.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] The collinear entanglement scheme used in this invention makes the optical path simpler and easier to understand, easier to adjust, and more integrated. While ensuring simplicity, this invention also helps to better demonstrate experimental phenomena and principles.

[0041] This invention integrates the optical path and the coincidence counter into a double-layer structure. After the optical path is adjusted, it is fixed on the housing. Students do not need to make tedious adjustments to the optical path during the experiment. They only need to rotate the polarizer of the polarization state detection system to observe the change in the experimental count, which further verifies the CHSH inequality. This improves the efficiency of the experiment and increases the students' participation, making it easier for students to better understand quantum entanglement.

[0042] This invention integrates the optical and electronic systems inside the housing and embeds the light source, thus confining the high-intensity laser to a fixed position, further improving the safety of the device and making it more suitable for teaching at the secondary and undergraduate levels.

[0043] This invention not only updates the traditional physics experiment teaching content and enhances the depth and difficulty of the course, but also provides a useful exploration and attempt to cultivate college students' innovative practical abilities.

[0044] The experimental kit designed in this invention is easy to operate and learn; it has a high degree of integration, which can meet a variety of experimental needs; it has strong stability, which ensures the accuracy of experimental results; the experimental phenomena are intuitive and clear, which helps students better understand entanglement phenomena; and it is easy for students to operate it themselves, thus cultivating their practical skills. Attached Figure Description

[0045] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0046] Figure 1 This is an optical path diagram of the interior of the upper housing shown in this invention;

[0047] Figure 2 This is a structural diagram of the interior of the lower housing shown in this invention;

[0048] Figure 3 This is a structural diagram of the collinear entanglement teaching system based on BS spectral splitting technology shown in this invention;

[0049] Figure 4 This is a schematic diagram of the collinear entanglement teaching system based on BS spectral splitting technology shown in this invention;

[0050] Figure 5 This is the operating interface of the host computer software operating system shown in this invention. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0052] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0053] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0054] Example 1

[0055] like Figure 1 , Figure 2As shown, this embodiment provides a collinear entanglement teaching experiment box based on BS spectral splitting technology, including a quantum light source system, a walk-off compensation system, and a polarization state detection system installed in the upper box, and an electronic control system installed in the lower box.

[0056] The quantum light source system includes a laser (A1) for generating continuous pump light with a wavelength of 405 nm; the laser generates a laser spectrum with a full width at half maximum (FWHM) of 0.9–1.1 nm and a vertical polarization state.

[0057] The quantum light source system includes a focusing lens (A2) and a polarization beamsplitter (A3). The focusing lens focuses the pump light onto a nonlinear crystal, where a spontaneous parametric down-conversion effect occurs. The polarization beamsplitter separates horizontally polarized |H> light and vertically polarized |V> light from the light source. The |H> light passes through the beamsplitter and reaches the optical trash can (A4), while the |V> light passes through the beamsplitter and reaches the nonlinear crystal. The nonlinear crystal is a barium borate crystal (BBO) (A5) used to generate type II entanglement, with a cut angle of 41.9°. After passing through the BBO, the light source is transformed from a single photon with polarization state |V> into two correlated photon pairs with polarization states |H> and |V> respectively. The light source is then split by a beamsplitter (A6), with both beams exiting the beams being... That is, when one of the light paths is |H> light, the other light path must be |V> light, thus creating entanglement.

[0058] Among them, the quantum light source consists of two entangled beams that are collinear with the pump light.

[0059] The walk-off compensation system includes a half-wave plate (B1), a half-wave plate (B2), a secondary BBO crystal (B3), and a secondary BBO crystal (B4), used to compensate for the walk-off of the two parametric beams in time and space, so as to improve the entanglement of the two beams; the walk-off compensation system also includes a reflector (B5) and a reflector (B6), all of which are placed at 45° to keep the optical path horizontal and vertical, which facilitates the adjustment of the optical path and reduces the length of the optical path in the same direction, making it easier to integrate. The optical path is then reflected to the polarization state detection system after passing through the reflector.

[0060] The polarization state detection system includes a polarizer (C1), a polarizer (C2), a filter (C3), a filter (C4), an optical fiber coupler (C5), an optical fiber coupler (C6), and optical fibers (C7) and (C8), which are used to perform quantum state tomography and fidelity measurement on the polarization state of photons and to detect light.

[0061] The polarization state detection system examines the polarization state of photons by rotating a polarizer to different angles, and is used to verify the CHSH inequality.

[0062] The electronic control system includes a single-photon detector (D1), a single-photon detector (D2), a voltage adapter board (D3) for connecting the power supply, and a coincidence counter (D4). The electronic control system is connected to the polarization state measurement system via optical fibers (C7) and (C8).

[0063] The experimental box is equipped with a power switch, a power input port, and a data transmission port. The power switch is used to control the on / off state of the laser, the first single-photon detector, the second single-photon detector, and the coincidence counting control device.

[0064] Example 2

[0065] like Figure 3 , Figure 4 As shown, this embodiment provides a collinear entanglement teaching system based on BS spectral splitting technology, including the collinear entanglement teaching experiment box based on BS spectral splitting technology described in Embodiment 1 and a host computer, wherein the host computer is connected to an electronic control system.

[0066] The host computer includes: a quantum entanglement experiment principle demonstration module, used to demonstrate the quantum entanglement experiment principle and the operation process of the collinear entanglement teaching experiment box; a real-time experimental data display module, used to display the experimental data of the collinear entanglement teaching experiment process; and a historical experiment record display module, used to display the experimental records of historical collinear entanglement teaching experiments.

[0067] Specifically, the quantum light source system includes a laser (A1) for generating continuous pump light with a wavelength of 405 nm; the laser generates a laser spectrum with a full width at half maximum (FWHM) of 0.9-1.1 nm and a vertical polarization state; the quantum light source system includes a focusing lens (A2) and a polarization beam splitter (A3), the focusing lens being used to focus the pump light onto a nonlinear crystal, subsequently resulting in a spontaneous parametric down-conversion effect; the polarization beam splitter is used to separate horizontally polarized |H> light and vertically polarized |V> light in the light source, wherein the |H> light reaches the optical garbage bin (A4) after passing through the polarization beam splitter, and the |V> light reaches the nonlinear crystal after passing through the polarization beam splitter; the nonlinear crystal is a barium borate crystal (BBO) (A5) used to generate type II entanglement, with a cut angle of 41.9°, after passing through the BBO, the light source is transformed from a photon with a polarization state of |V> into two correlated photon pairs with polarization states of |H> and |V> respectively; the light source is then split by a beam splitter (A6), and the light from both paths of the beam splitter is... That is, when one of the light paths is |H> light, the other light path must be |V> light, thus creating entanglement.

[0068] The walk-off compensation system includes a half-wave plate (B1), a half-wave plate (B2), a secondary BBO crystal (B3), and a secondary BBO crystal (B4), used to compensate for the walk-off of the two parametric beams in time and space, so as to improve the entanglement of the two beams; the walk-off compensation system also includes a reflector (B5) and a reflector (B6), all of which are placed at 45° to keep the optical path horizontal and vertical, which facilitates the adjustment of the optical path and reduces the length of the optical path in the same direction, making it easier to integrate. Then the optical path is reflected to the polarization state detection system after passing through the reflector.

[0069] The polarization state detection system includes a polarizer (C1), a polarizer (C2), a filter (C3), a filter (C4), an optical fiber coupler (C5), an optical fiber coupler (C6), and optical fibers (C7) and (C8), which are used to perform quantum state tomography and fidelity measurement on the polarization state of photons and to detect light.

[0070] The polarization state measurement system detects the polarization state of photons and collects the data to the electronic control system by rotating polarizers (C1) and (C2) to different angles.

[0071] The host computer is connected to the electronic control system, outputs experimental data corresponding to different polarization operations of photons by the polarization state measurement system, and verifies the entanglement fidelity and CHSH inequality.

[0072] Figure 1 In the diagram, A represents the quantum light source. After passing through a lens (A2) and then through a laser (A1), the light is focused onto a BBO crystal (A5). After passing through the BBO, the light source changes from a single photon with polarization state |V> to two correlated photon pairs with polarization states |H> and |V> respectively. The beam is then split by a beam splitter (A6) to generate type II polarization entanglement. When one beam is |V>, the other beam must be |H>, and when one beam is |H>, the other beam must be |V>, thus creating entanglement. In this embodiment, Figure 2 In the diagram, B represents the quantum light source walk-off compensation section. When the two photons pass through the main BBO, they experience walk-off in both time and space due to the birefringence effect. To compensate for walk-off, the two entangled photons pass sequentially through half-wave plates (B1), half-wave plates (B2), secondary BBO crystals (B3), secondary BBO crystals (B4), and mirrors (B5) and (B6). The half-wave plates are rotated to a position 45 degrees to their fast axis to convert |H> light and |V> light into each other. The secondary BBO is used to align the walk-off directions with each other, thereby completing walk-off compensation and improving the entanglement degree. C represents the polarization state detection system, which uses polarizers (C1) and (C2) to measure the change in coincidence count of the two parametric lights under different polarization states.

[0073] like Figure 5The diagram shows the control panel of the host computer software operating system. Alice and Bob represent the number of photons received by the two single-photon detectors per second, respectively. Alice & Bob represent the number of photons arriving simultaneously at both single-photon detectors per second. The efficiency is the proportion of Alice & Bob's data per second to the total number of photons in the current time period. Simultaneously, the polarization state of entangled photon pairs is measured by rotating the angle of the polarizer in the polarization state detection system. Under the |H> and |V> basis vectors, Alice & Bob has a minimum value when the angles of polarizers (C1) and (C2) are both 0° or both are 90°. When the angles of polarizers (C1) and (C2) are 0° and 90°, and 90° and 0°, respectively, Alice & Bob has a maximum value, and the ratio of the maximum to the minimum value is greater than 15:1. Under the |+> and |-> basis vectors, Alice & Bob has a maximum value when the angles of polarizers (C1) and (C2) are both 45°. When the angles of polarizers (C1) and (C2) are 45° and 135°, and 135° and 45°, respectively, Alice & Bob has a minimum value, and the ratio of the maximum to the minimum value is greater than 7:1. Therefore, the CHSH inequality can be measured.

[0074] Example 3

[0075] This embodiment provides a collinear entanglement teaching method based on BS spectral splitting technology, employing the collinear entanglement teaching system based on BS spectral splitting technology described in Embodiment 2, including:

[0076] Adjust all components to their initial state, and connect the power supply to both the collinear entanglement teaching experiment box and the host computer.

[0077] Remove the polarization beam splitter, the laser emits laser light, and the initial coincidence count value of the coincidence counter is recorded;

[0078] A polarization beam splitter is installed, and the laser emits laser light. The polarization state of the photons is checked by rotating the polarizer to different angles, which is used to verify the CHSH inequality.

[0079] Record the number of photons received by the first and second single-photon detectors, as well as the coincidence count.

[0080] The process of verifying the CHSH inequality by rotating a polarizer to different angles to check the polarization state of photons includes:

[0081] Under the basis vectors |H> and |V>, Alice & Bob has a minimum value when the angles of the two polarizers are both 0° or both are 90°, and a maximum value when the angles of the two polarizers are 0° and 90° and 90° and 0° respectively, and the ratio of the maximum value to the minimum value is greater than 15:1.

[0082] Under the |+> and |-> basis vectors, Alice & Bob has a maximum value when the angles of the two polarizers are both 45°, and a minimum value when the angles of the two polarizers are 45° and 135° and 135° and 45° respectively, and the ratio of the maximum value to the minimum value is greater than 7:1; so as to perform CHSH inequality measurement.

[0083] Alice & Bob represent the number of photons arriving at both single-photon detectors simultaneously per second.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A collinear entanglement teaching experiment box based on BS spectrophotometry, characterized in that, The system includes a lower housing and an upper housing. An electronic control system is installed in the lower housing, and a quantum light source system, a walk-off compensation system, and a polarization state detection system are installed in the upper housing, arranged sequentially along the optical path. The electronic control system is connected to the polarization state detection system via an optical fiber. The quantum light source system includes a laser, a focusing lens, and a polarization beam splitter arranged sequentially along the optical path. After being split by the polarization beam splitter, one beam of light enters the optical trash can, and the other beam passes sequentially through a barium borate crystal and the beam splitter. The walk-off compensation system includes two identical optical paths, each of which includes a half-wave plate, a secondary BBO crystal, and a reflector arranged sequentially. The polarization state detection system includes two identical optical paths, each of which includes a polarizer, a filter, and an optical fiber coupler arranged sequentially. The electronic control system includes a first single-photon detector, a second single-photon detector, and a coincidence counter, wherein both the first and second single-photon detectors are connected to the coincidence counter.

2. The collinear entanglement teaching experiment box based on BS spectral splitting technology according to claim 1, characterized in that, The laser is used to generate continuous pump light with a wavelength of 405 nm and a vertical polarization state. Alternatively, the polarization beam splitter is used to separate the |H> light and |V> light in the light source; Alternatively, the optical trash can is used to collect |H> light; Alternatively, the barium metaborate crystal is used to convert a photon with polarization state |V> into two correlated photon pairs with polarization states |H> and |V> respectively; Alternatively, the beam splitter is used to split the |H>|V> light into two paths; one path is the |H> light and the other path is the |V> light.

3. The collinear entanglement teaching experiment box based on BS spectral splitting technology according to claim 1, characterized in that, The walk-off compensation system is used to compensate for the time and space walk-off of light when it passes through a barium borate crystal.

4. The collinear entanglement teaching experiment box based on BS spectral splitting technology according to claim 1, characterized in that, Both of the aforementioned mirrors are positioned at 45° to maintain the horizontal and vertical alignment of the light path.

5. The collinear entanglement teaching experiment box based on BS spectral splitting technology according to claim 1, characterized in that, The polarization state detection system is used to examine the polarization state of photons by rotating a polarizer to different angles, and is used to verify the CHSH inequality.

6. The collinear entanglement teaching experiment box based on BS spectral splitting technology according to claim 1, characterized in that, The experimental box is equipped with a power switch, a power input port, and a data transmission port. The power switch is used to control the on / off state of the laser, the first single-photon detector, the second single-photon detector, and the coincidence counting control device.

7. A collinear entanglement teaching system based on BS spectrophotometry, characterized in that, The invention includes a collinear entanglement teaching experiment box based on BS spectral splitting technology and a host computer as described in any one of claims 1-6, wherein the host computer is connected to an electronic control system.

8. The collinear entanglement teaching system based on BS beam splitting technology according to claim 7, characterized in that, The host computer includes: The quantum entanglement experiment principle demonstration module is used to demonstrate the experimental principle of quantum entanglement and the operation process of the collinear entanglement teaching experiment box; The real-time experimental data display module is used to display experimental data during the collinear entanglement teaching experiment. The historical experiment record display module is used to display the experimental records of historical collinear entanglement teaching experiments.

9. A collinear entanglement teaching method based on BS spectrophotometry, characterized in that, The collinear entanglement teaching system based on BS beam splitting technology as described in any one of claims 7-8 includes: Adjust all components to their initial state, and connect the power supply to both the collinear entanglement teaching experiment box and the host computer. Remove the polarization beam splitter, the laser emits laser light, and the initial coincidence count value of the coincidence counter is recorded; A polarization beam splitter is installed, and the laser emits laser light. The polarization state of the photons is checked by rotating the polarizer to different angles, which is used to verify the CHSH inequality. Record the number of photons received by the first and second single-photon detectors, as well as the coincidence count.

10. The collinear entanglement teaching method based on BS beam splitting technology according to claim 9, characterized in that, The process of verifying the CHSH inequality by rotating a polarizer to different angles to check the polarization state of photons includes: Under the basis vectors |H> and |V>, Alice & Bob has a minimum value when the angles of the two polarizers are both 0° or both are 90°, and a maximum value when the angles of the two polarizers are 0° and 90° and 90° and 0° respectively, and the ratio of the maximum value to the minimum value is greater than 15:

1. Under the |+> and |-> basis vectors, Alice & Bob has a maximum value when the angles of the two polarizers are both 45°, and a minimum value when the angles of the two polarizers are 45° and 135° and 135° and 45° respectively, and the ratio of the maximum value to the minimum value is greater than 7:1; so as to perform CHSH inequality measurement. Alice & Bob represent the number of photons arriving at both single-photon detectors simultaneously per second.

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