Method and system for realizing quantum state tomography on polarization entangled states based on dielectric metasurfaces

Abstract

The application provides a method for realizing quantum state tomography of N-photon polarization entangled states based on a dielectric metasurface, comprising the following steps: providing N light paths, and arranging one same metasurface on each light path; the metasurface comprises four regions with different optical responses, and is used for extracting different polarization components of incident light and only existing zero-order diffraction, and a complete polarization projection base is formed through the outputs of different regions; N photons in an N-photon quantum state are input into the N light paths in sequence, and irradiate onto each region of each metasurface, so that the polarization entangled state is projected onto four N different polarization projection bases; and the density matrix of the N-photon polarization entangled state is reconstructed through coincidence measurement. The application further discloses a corresponding system. Through the application, high-fidelity quantum state tomography can be realized, and the integration and miniaturization of a quantum optics system are facilitated.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement technology, specifically a technique for quantum state tomography of polarization entangled states through a metasurface of a medium. Background Technology

[0002] In multiphoton quantum optics, quantum state tomography often characterizes the quantum state by projecting measurements onto a complete projection basis. In quantum state tomography of multiphoton polarized entangled states, each photon passes through a combination of quarter-wave plates, half-wave plates, and polarizers or polarization beam splitters with different rotation angles, effectively projecting the multiphoton polarized entangled state onto a specific polarization projection basis. Then, coincidence measurements are performed on the multiphotons, and algorithms such as maximum likelihood estimation are used to reconstruct the density matrix of the multiphoton state. Important parameters can be extracted from the density matrix to characterize the quantum state, such as fidelity, which describes the distance between two quantum states.

[0003] Metasurfaces are two-dimensional metamaterials composed of artificially designed subwavelength structural units, enabling precise manipulation of the amplitude, phase, polarization, and wavefront of light at the subwavelength scale. In recent years, dielectric metasurfaces have been applied to quantum optics research, including quantum entanglement generation, tunable two-photon interference, quantum imaging, dynamic manipulation of quantum states, weak measurement, and quantum state reconstruction. In quantum state reconstruction research, a three-layer interlaced metagrating has been designed to achieve multiphoton quantum state tomography, thereby reconstructing quantum states without relying on traditional waveplates and polarization beam splitters. However, the overall size of the interlaced metagrating remains on the millimeter scale. More seriously, the combination of the corresponding two diffraction channels results in a diffraction efficiency of less than 30% compared to the incident light energy. Therefore, more compact and efficient new methods are needed, which are crucial for the future development of integrated photonic systems. Summary of the Invention

[0004] This invention proposes a quantum state tomography method based on a dielectric metasurface to realize polarization entangled states. It achieves high-fidelity quantum state tomography of arbitrary polarized photon pairs using a single, two, or more dielectric metasurfaces with high transmission coefficients (hereinafter referred to as "metasurfaces"). The metasurface used in this invention has four regions, each capable of extracting a specific polarization component of the incident light and exhibiting only zero-order diffraction. The outputs of the four regions constitute a complete polarization projection basis for a single photon. Furthermore, this invention also discloses a system corresponding to the above method.

[0005] The first aspect of this invention proposes a method for quantum state tomography of N-photon polarization entangled states based on a metasurface, comprising: providing N optical paths, where N is an integer greater than or equal to 2; each optical path having an identical metasurface comprising four regions with different optical responses, each region being used to extract different polarization components of incident light and exhibiting only zero-order diffraction, and forming a complete polarization projection basis through the outputs of the four regions; inputting N photons from the N-photon quantum state into the N optical paths, sequentially irradiating each region of each metasurface, thereby projecting the polarization entangled state onto the four regions. N A number of different polarization projection bases are used; the density matrix of the N-photon polarization entangled state is reconstructed by coincidence measurement.

[0006] Optionally, the entangled state is projected onto different polarization bases, and the density matrix of the N-photon polarization entangled state is reconstructed through coincidence measurement. Specifically, this includes: converting the emitted light signals through each metasurface into N electrical signals; performing coincidence counting on the N electrical signals; and reconstructing the density matrix of the unknown polarization entangled state based on the coincidence measurement.

[0007] Optionally, the emitted light from each metasurface is collected to a single-photon photodetector, and the optical signal is converted into an electrical signal by the single-photon photodetector; N electrical signals are input to a coincidence counter, and the coincidence count is obtained by the coincidence counter; based on the coincidence measurement, the density matrix of the unknown two-photon polarization entangled state is reconstructed by a maximum likelihood estimation algorithm.

[0008] A second aspect of the present invention proposes a system for quantum state tomography of polarization entangled states based on a metasurface of a medium, which is used for quantum state tomography of N-photon polarization entangled states, where N is an integer greater than or equal to 2; the quantum state tomography system includes N optical paths, and a metasurface, a single-photon detector and a coincidence counter are arranged sequentially along the incident light direction of the optical paths; the metasurface includes four regions with different optical responses, the four regions are respectively used to extract different polarization components of the incident light and only zero-order diffraction exists, and a complete polarization projection basis is formed through the output of the four regions.

[0009] Optionally, the optical path further includes a first lens and a second lens arranged on both sides of the metasurface along the optical path direction; the first lens is used to focus the incident light onto a corresponding area of ​​the metasurface; the second lens is used to convert the outgoing light from the metasurface into parallel light output.

[0010] Optionally, the optical path may further include an optical fiber coupler disposed between the metasurface and the single-photon detector.

[0011] Based on the first and second aspects of the present invention:

[0012] Optionally, each region of the metasurface has a rectangular array of periodically arranged structural units, the period of which is less than the wavelength of the incident light; the structural units include two types of nanopillars.

[0013] Optionally, the transmittance of the four regions in the metasurface is all in the range of 92% to 97%.

[0014] Optionally, in the metasurface, under orthogonally polarized light incident light, the extinction ratio of any region exceeds 40.

[0015] Optionally, the metasurface is made of any one of the following materials: amorphous silicon, monocrystalline silicon, titanium dioxide, gallium nitride, and silicon nitride.

[0016] The present invention has the following beneficial effects:

[0017] (1) This invention combines dielectric metasurfaces with quantum optics for the study of quantum state tomography, achieving quantum state tomography (N≥2) of N-photon polarization entangled states. Dielectric metasurfaces have the advantage of low loss, and their preparation method is compatible with complementary metal-oxide-semiconductor processes, providing feasibility for miniaturization and integration of photonic devices.

[0018] (2) The present invention can replace the combination of traditional 1 / 4 wave plate, 1 / 2 wave plate and polarization beam splitter with metasurface, which can not only reduce the number of traditional optical elements in quantum state tomography, but more importantly, significantly reduce the system size, which is beneficial to the integration and miniaturization of quantum optical systems.

[0019] (3) The medium metasurface used in the present invention has very low loss. Under single-photon source incident, the average transmission efficiency of the four regions can reach up to 96%, and the loss during polarization projection measurement is minimal, which is of practical significance for the measurement of quantum states.

[0020] (4) This invention uses a transmissive metasurface to realize quantum state tomography of N-photon polarization entangled states and reconstructs the density matrix of entangled states. Based on the density matrix obtained by the metasurface measurement, we obtained the fidelity, trace distance and von Neumann entropy. The results are almost consistent with those obtained by the traditional scheme, which will help to further realize miniaturized and integrated quantum information processing photonic platforms. Attached Figure Description

[0021] Figure 1 : This is a schematic diagram of two identical metasurfaces (metasurface 1 and metasurface 2) used in the embodiment to achieve quantum state tomography of polarization entangled states.

[0022] Figure 2 : These are scanning electron microscope images and transmission spectra of the metasurface in the embodiments, wherein: Figure 2 a- Figure 2 d represents scanning electron microscope images of four different regions (metasurface 1-1, metasurface 1-2, metasurface 1-3 and metasurface 1-4) in amorphous silicon metasurface 1, with a scale bar of 400 nm. Figure 2 e- Figure 2 h represents the transmission spectra of four different regions in metasurface 1 obtained by experimental measurement, with the wavelength range of incident light being 770-850 nm. T γ,δ This represents the transmission spectrum where the incident light is γ-polarized and the outgoing light is δ-polarized.

[0023] Figure 3 : A schematic diagram of an experimental setup for quantum state tomography of polarization entangled states using conventional optical elements and by replacing a conventional optical element on a path with a metasurface 1.

[0024] Figure 4 a and Figure 4 b represents the basis. Figure 3 The experimental data obtained from the two schemes were used to reconstruct the real and imaginary parts of the polarization entanglement state density matrix.

[0025] Figure 5 : Schematic diagram of an experimental setup for quantum state tomography of polarization entangled states using only metasurfaces (metasurface 1 and metasurface 2).

[0026] Figure 6 Experimental results of quantum state tomography of polarization entangled states using only metasurfaces (metasurface 1 and metasurface 2). Figure 6 a to Figure 6 d corresponds to the four incident Bell states obtained by experimental measurement |Ψ + >、|Ψ - >、|Φ + > and |Φ - The real and imaginary parts of the density matrix; the imaginary part of the density matrix is ​​almost zero. Detailed Implementation

[0027] This invention presents a method for quantum state tomography of N-photon polarization states (N≥2) using a high-transmission-efficiency metasurface. The metasurface involved in this method comprises four regions, each functioning as a horizontal, vertical, -45° linear polarizer, and a right-handed circular polarizer, respectively. Different regions act as different polarization projection bases, and pairwise combinations of different regions on two metasurfaces constitute a complete polarization projection base. A complete polarization projection base refers to a base that, for N-photon polarization states (N≥2), has a quantum state tomography efficiency of 2... N ×2 N There are 2 polarization projection bases. N ×2 N matrix If this set of polarization projection bases satisfies This constitutes a complete polarization projection basis. For example, for a two-photon polarization state, a matrix with 4×4 polarization projection bases can be found. If this set of polarization projection bases satisfies This constitutes a complete polarization projection basis. Each region of the metasurface is designed with an array of nanostructures to achieve different polarization functions. These nanostructure arrays consist of periodically arranged nanostructure units, where the period is smaller than the wavelength; therefore, the metasurface exhibits only zero-order diffraction. It should be noted that the functions of the four regions of the metasurface are not limited to the above combinations. They can also be horizontal, vertical, 45° linear polarizers and left-handed circular polarizers, or combinations of right-handed circular polarizers, left-handed circular polarizers, horizontal polarizers, and 45° linear polarizers, as long as a complete polarization projection basis can be formed.

[0028] Furthermore, we achieved high-fidelity quantum state tomography of polarization-entangled states using single-piece and combinations of traditional optical elements, as well as combinations of two metasurfaces. This measurement scheme can replace traditional quarter-wave plates, half-wave plates, and polarization beam splitters, reducing the number of traditional optical elements in quantum state tomography, significantly decreasing system size, and facilitating the integration and miniaturization of quantum optical systems.

[0029] For incident light in the wavelength range of 770–850 nm, we use amorphous silicon as the material system for the metasurface. Amorphous silicon is a high-performance dielectric material, exhibiting extremely low loss and a high refractive index within this wavelength range. Under single-photon source incident at a wavelength of 810 nm, the average transmission efficiency of this metasurface reaches 96%, with minimal loss during polarization projection measurement, which is of practical significance for current quantum state measurements. However, the material for the metasurface is not limited to amorphous silicon; other dielectric materials such as single-crystal silicon, titanium dioxide, gallium nitride, and silicon nitride can also be used, with the specific selection based on the incident light wavelength. When selecting the dielectric material, we aim to ensure that the transmission coefficients of different regions on the metasurface are as close as possible, and the higher the transmission coefficient, the better. For example, we can limit the selected dielectric material to ensure that the transmittance of each region is within the range of 92%–97%. In this embodiment of the invention, we use amorphous silicon as the dielectric material, resulting in an average transmission efficiency of 96% across all regions of the metasurface.

[0030] Combination Figure 1 As shown, we designed two identical medium metasurfaces (metasurface 1 and metasurface 2). Each metasurface consists of four regions with different optical responses, thereby utilizing the outputs of different regions of the metasurface to form a complete polarization projection base (i.e., horizontal, vertical, -45° linear polarization and right-hand circular polarization constitute a complete polarization projection base). Figure 1 In this design, metasurfaces 1-1, 1-2, 1-3, and 1-4 act as horizontal (|H>), vertical (|V>), -45° linear polarization (|A>), and right-handed circular polarization (|R>), respectively. Each region has an array of silicon nanopillars, and the regions are relatively independent. The structural units in each silicon nanopillar array include two different types of silicon nanopillars. These two types of silicon nanopillars may have different cross-sectional shapes (e.g., rectangular, elliptical, triangular, polygonal, and irregular shapes), or the same cross-sectional shape but different sizes, or different angles, but the heights of these silicon nanopillars are usually the same. The coherent superposition of the scattered fields of each silicon nanopillar in each region results in only zero-order diffracted light, which can project the incident light to a specific polarization state, such as linear polarization and circular polarization. It is worth noting that since the different regions of the metasurfaces are independent of each other, this invention does not impose special requirements on the structure, size parameters, and arrangement of the specific structural units in each region, as long as the functional requirements are met.

[0031] Assuming that a single photon with arbitrary polarization is sequentially incident on four regions of a metasurface (the specific order of incident is not required, as long as each region is incident), in other words, it is equivalent to projecting the polarization state of the single photon, whose incident quantum state is unknown, onto four different polarization projection bases. They are respectively represented as By measuring the intensity of emitted light on different polarization projection bases, the density matrix of single-photon quantum states can be reconstructed.

[0032] When the incident quantum state is an unknown form of two-photon polarization entangled state, we can reconstruct its quantum state density matrix based on two identical metasurfaces 1 and 2. Assuming that the two photons in the entangled photon pair are sequentially irradiated by different regions of metasurfaces 1 and 2, the entangled state will be simultaneously projected onto the polarization projection basis. and And constitute a complete set of polarization projection bases, totaling That is, 16 polarization projection bases. First, photons are coupled into an optical fiber via an optical fiber coupler, then input into a single-photon detector via the optical fiber to convert the optical signal into an electrical signal. Finally, the electrical signal is input to a coincidence counter, which provides the coincidence count. Through 16 coincidence measurements, the density matrix of the entangled state with arbitrary polarization that meets physical requirements is reconstructed using a maximum likelihood estimation algorithm. The fidelity of the incident two-photon state is then obtained from the reconstructed density matrix.

[0033] The following specific embodiments and accompanying drawings further illustrate the present invention:

[0034] Combination Figure 2 As shown in Example 1, we prepared an amorphous silicon metasurface sample using a standard electron beam etching process. Each of the four regions of the metasurface has a rectangular array of silicon nanopillars. The period of the rectangular array is much smaller than the wavelength of the incident light, thus only zero-order diffraction exists, satisfying the condition that different regions correspond to different polarizers. We considered the interaction between light and the periodically arranged silicon nanopillars. The structural unit of the sample contains two types of nanopillars. The coherent superposition of the scattered fields from each nanopillar in each region generates the required light beam. Different regions act as horizontal, vertical, -45° linear polarizers, and right-handed circular polarizers, respectively. Scanning electron microscope images (front view and side view) of the four different regions are shown below. Figure 2 a to Figure 2 As shown in d. In the xy plane, Figure 2 The white dashed boxes represent structural units in different regions of the metasurface. A coordinate system is established with the upper left corner of the white dashed boxes as the origin, where p represents the period. The centers of the two silicon nanopillars in each structural unit are located at (p / 4, p / 4) and (3p / 4, 3p / 4), respectively. The period p of the structural unit along the x and y directions is 400–500 nm, and the height of the two nanopillars is 400–600 nm. It should be noted that the periods of the structural units along the x and y directions can be the same or different, and the heights of the various nanopillars included on the metasurface can be consistent or inconsistent. This invention does not impose any limitations on this, but to simplify the fabrication process, the height of all nanopillars on the metasurface can be standardized. Figure 2 a to Figure 2 As shown in Figure c, the first type of nanopillar in the structural unit has a length of 180–250 nm and a width of 100–150 nm, while the second type has a length of 120–250 nm and a width of 100–150 nm. This means that the structural units in the three regions 1-1, 1-2, and 1-3 of the metasurface contain only two sizes of rectangular nanopillars. Three different structural units are formed by different arrangements and angles of these rectangular nanopillars. Figure 2 As shown in Figure d, the first type of nanopillar in its structural unit has a length of 180–250 nm and a width of 100–160 nm, while the second type of nanopillar has a length of 120–250 nm and a width of 90–150 nm. Through the above design, the four regions of the metasurface can respectively realize the functions of different polarizers, such as linear polarizers and circular polarizers.

[0035] Next, we experimentally verified the function of the metasurface described above. We measured the transmission spectrum of metasurface 1 at incident light wavelengths of 770-850 nm using a spectrophotometer. (See attached image.) Figure 2 e to Figure 2 h. At an incident light wavelength of 810 nm, the transmission coefficient T of the metasurface 1-1 is... x，x 96% Figure 2 (The solid line in e); the transmission coefficient T of metasurface 1-2 y，y 96% Figure 2 (dashed line in f); Transmission coefficient T of metasurface 1-3 -45°,-45° 97% Figure 2 (solid line in g); in metasurfaces 1-4, the transmission coefficient T x，x T x，y T y，x T y，y Almost equal ( Figure 2 h), the phase difference between the x- and y-linearly polarized components under x-linearly polarized and y-linearly polarized incident light is 92° and 97° respectively (metasurface 1-4), which means that the transmitted light is in a better circularly polarized state.

[0036] Referring to Table 1, we also verified that when a single photon with a wavelength of 810 nm is incident on different regions of metasurface 1, different regions of the metasurface can act as different polarizers. We define the photon counting extinction ratio T. α / T β (abbreviated as "extinction ratio"), where α and β are the polarization states of the incident single photon, and T is the polarization ratio of the incident single photon. α and T β The extinction ratios are the coincidence counts of α- and β-polarized light incident on the same region of the metasurface. Table 1 shows the extinction ratios of four independent regions in metasurface 1. For metasurface 1-1, α and β correspond to horizontal and vertical linear polarization, respectively; for metasurface 1-2, α and β correspond to vertical and horizontal linear polarization, respectively; for metasurface 1-3, α and β correspond to -45° and 45° linear polarization, respectively; and for metasurface 1-4, α and β correspond to right-handed and left-handed circular polarization, respectively. Therefore, we can see that the extinction ratio characterizes the performance of different regions of the metasurface. Ideally, the extinction ratio should be infinite; a higher extinction ratio means that the region exhibits a more perfect polarizer. As shown in Table 1, we experimentally measured the highest extinction ratio of metasurface 1 to be 254:1, and the lowest to be over 43:1. The higher extinction ratios indicate that the prepared metasurface 1 is a relatively perfect polarizer.

[0037] Table 1

[0038]

[0039] Furthermore, Example 2 discloses the specific application of the metasurface described in Example 1 in quantum state tomography and the corresponding system. To achieve quantum state tomography, we place metasurface 1 along one of the paths of the entangled light source (the black dashed box), as shown... Figure 3As shown, when an arbitrary polarization-entangled photon pair is incident, the center wavelength of the photon pair is 810 nm. One photon in the photon pair is projected onto four sets of polarization projection bases by passing through a combination of quarter-wave plates, half-wave plates, and polarization beam splitters with different rotation angles (path III, conventional optical elements). At the same time, the other photon passes through a lens and is then focused sequentially onto quarter-wave plates, half-wave plates, and polarization beam splitters with different rotation angles (path I, conventional optical elements), or by translating a three-axis displacement stage so that the photon sequentially passes through four different regions of metasurface 1 (path II, metasurface 1), interacting with different regions of the metasurface to achieve the projection of the photon onto the four sets of polarization projection bases. Photons emitted via path III are transmitted to an optical fiber coupler where they are coupled into the optical fiber. The optical fiber then transmits the photons to a single-photon detector, where the optical signal is converted into an electrical signal. Photons emitted via path I or path II are first converted into parallel light by a lens, and then sequentially transmitted to an optical fiber coupler and a single-photon detector, where the optical signal is converted into an electrical signal. The incident two-photon state is projected onto 16 sets of polarization projection bases. By measuring the coincidence count between two single-photon detectors, we can perform 16 coincidence measurements on the entangled state. The density matrix of the unknown polarization entangled state can then be reconstructed using the maximum likelihood estimation algorithm. It should be noted that the lens is not a necessary component in the above optical path; its main function is focusing. When the surface area of ​​the metamaterial is large, the lens may not be required.

[0040] Specifically, when the incident entangled state is one type of Bell state We are looking at a Bell state |Ψ + >Perform quantum state tomography. Figure 4 These are the experimental results we obtained. Based on traditional optical elements (path I, quarter-wave plate, half-wave plate, and polarization beam splitter), we obtained 16 coincidence counts, which can reconstruct the density matrix of the two-photon state, such as... Figure 4 As shown in Figure a, the experiment yielded a fidelity of 96.70% for the entangled light source. Next, we switched to path II, replacing one of the traditional optical elements with metasurface 1. When one photon from an entangled photon pair passes through the lens, the photon is sequentially focused onto four different regions of metasurface 1, as shown in Figure a. Figure 4 As shown in b, the Bell state |Ψ is experimentally reconstructed through 16 coincidence measurements using quantum state tomography and maximum likelihood estimation algorithms. +The real and imaginary parts of the density matrix have a fidelity of 95.87%. Based on the experimental measurements described above, two sets of density matrices were obtained. From these density matrices, we obtained the fidelity, trace distance, and von Neumann entropy, as shown in Table 2. It can be seen from the table that the fidelity, trace distance, and von Neumann entropy obtained using metasurface 1 and another conventional optical element measurement scheme are slightly lower than those obtained using the conventional measurement scheme. This may be due to imperfections in the structural dimensions during the metasurface fabrication process. However, the results confirm that metasurfaces can replace some conventional optical elements to achieve quantum state tomography of polarization-entangled states.

[0041] Table 2

[0042]

[0043] In Example 2, we demonstrated that metasurfaces can replace some traditional optical elements for quantum state tomography of polarization-entangled states. In Example 3, we used two identical metasurfaces (metasurface 1 and metasurface 2) to achieve quantum state tomography. The quantum state tomography system disclosed in Example 3 includes two identical optical paths, specifically including lens 1, metasurface 1 or metasurface 2, lens 2, fiber coupler, and single-photon detector arranged sequentially along the optical path direction. Entangled photon pairs pass through lens 1 and are focused sequentially into four different regions of metasurface 1 and metasurface 2. Then, the photons pass through lens 2 and become parallel light, which is then sequentially transmitted to the fiber coupler and single-photon detector. Finally, a coincidence measurement is performed by a coincidence counter. Figure 5 As shown, the incident quantum state can be any two-photon polarization entangled state; here we take four Bell states ( and Taking entangled photons as an example, we can obtain 16 coincidence counts by translating a three-axis stage and having the incident entangled photon pairs interact with various regions on the two metasurfaces. Then, we can reconstruct the density matrix of each Bell state using quantum state tomography and maximum likelihood estimation algorithms. Figure 6 a to Figure 6 As shown in d. Four Bell states |Ψ were experimentally measured. + >、|Ψ - >、|Φ + > and |Φ - The fidelities of the four Bell states were 93.45%, 96.86%, 96.34%, and 94.58%, respectively. Using conventional optical elements (quarter-wave plate, half-wave plate, and polarizing beam splitter), we measured the fidelities of the four Bell states to be 96.70%, 97.44%, 98.13%, and 97.55%, respectively.

[0044] Based on the density matrix obtained from the experiment, we obtained the fidelity, trace distance, and von Neumann entropy, as shown in Table 3. We then compared the results obtained using the two methods. The table shows that the fidelity of the quantum state is almost always higher than 94% (metasurface), and higher than 96% (traditional device); the trace distance is almost always around 0.1 (metasurface), and around 0.07 (traditional device); the von Neumann entropy is almost always below 0.3 (metasurface), and below 0.2 (traditional device). The results indicate that the experimental results obtained by the two methods are almost identical, confirming the effectiveness of metasurfaces in quantum state tomography.

[0045] Table 3

[0046]

[0047] In summary, if we want to achieve quantum state tomography of N-photon polarization entangled states, N≥2, we need 3N conventional bulk optical elements, including quarter-wave plates, half-wave plates, and polarization beam splitters. However, based on the method proposed in this invention, only N identical metasurfaces are needed to construct 4 N A single polarization projection basis is sufficient to perform quantum state tomography. This method not only reduces the number of traditional optical components experimentally, but more importantly, it enables the miniaturization and integration of measurement elements. In our examples, we demonstrate that two metasurfaces can perform quantum state tomography on two-photon polarized entangled states, and the results obtained from metasurface measurements, such as density matrix, fidelity, trace distance, and von Neumann entropy, are almost identical to those obtained from traditional optical components. Therefore, we believe that with advancements in nanofabrication technology, silicon nanopillars with more precise geometry and sharper edges can be fabricated, which will facilitate the further miniaturization and integration of quantum information processing photonic platforms.

[0048] Finally, it should be noted that although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art, guided by this specification, can make many other forms without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for quantum state tomography of N-photon polarization entangled states based on a metasurface of a medium, characterized in that, include: Provide N optical paths, the N It is an integer greater than or equal to 2; each optical path is provided with an identical metasurface, which includes four regions with different optical responses, respectively used to extract different polarization components of the incident light and only zero-order diffraction exists. The outputs of the four regions form a complete polarization projection basis. Will N- In the quantum state of photons N Photons are input to N A series of optical paths sequentially illuminate different regions of each metasurface, enabling the polarization entangled state to be projected onto 4... N A different polarization projection base; Based on the polarization projection base, the result is reconstructed through coincidence measurement. N- The density matrix of photon polarization entangled states; Each region of the metasurface has a rectangular array of periodically arranged structural units, the period of which is less than the wavelength of the incident light. The structural units include two types of nanopillars; the two types of nanopillars differ in at least one aspect, such as cross-sectional shape, size parameters, or angle setting.

2. The method as described in claim 1, characterized in that, By projecting the entangled state onto different polarization bases and reconstructing the state through coincidence measurements, the entangled state is obtained. N- The density matrix of photon polarization entangled states specifically includes: The emitted light signals from each metasurface are converted into N Circuit signal; Will N The circuit signal is counted in coincidence. The density matrix of the unknown polarization entangled state is reconstructed based on the coincidence count.

3. The method as described in claim 2, characterized in that, The emitted light from each metasurface is collected by a single-photon detector, which converts the optical signal into an electrical signal. N electrical signals are input to a coincidence counter, which calculates the coincidence count. Based on the coincidence measurement, the density matrix of the unknown two-photon polarization entangled state is reconstructed using a maximum likelihood estimation algorithm.

4. A system for realizing quantum state tomography of polarization entangled states based on a dielectric metasurface, characterized in that, Used for N- Photon polarization entangled state quantum state tomography, the N It is an integer greater than or equal to 2; The quantum state tomography system includes N An optical path, the optical path comprising a metasurface, a single-photon detector and a coincidence counter arranged sequentially along the light incident direction; The metasurface includes four regions with different optical responses. The four regions are used to extract different polarization components of the incident light and only zero-order diffraction exists. The outputs of the four regions form a complete polarization projection base. Each region of the metasurface has a nanostructure array composed of periodically arranged structural units, the period of which is less than the wavelength of the incident light, and the structural units include two types of nanopillars; the two types of nanopillars differ in at least one aspect in terms of cross-sectional shape, size parameters, and angle setting.

5. The system as described in claim 4, characterized in that, In the metasurface, the transmittance of the four regions is all in the range of 92% to 97%.

6. The system as described in claim 4, characterized in that, In the metasurface, under orthogonally polarized light incident light, the extinction ratio of any region exceeds 40.

7. The system as described in claim 4, characterized in that, The metasurface is made of any one of the following materials: amorphous silicon, monocrystalline silicon, titanium dioxide, gallium nitride, and silicon nitride.

8. The system according to any one of claims 4 to 7, characterized in that, The optical path further includes a first lens and a second lens arranged on both sides of the metasurface along the optical path direction; the first lens is used to focus the incident light onto the corresponding area of ​​the metasurface; the second lens is used to convert the outgoing light from the metasurface into parallel light output.

9. The system according to any one of claims 4 to 7, characterized in that, The optical path also includes an optical fiber coupler arranged between the metasurface and the single-photon detector.

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