High-dimensional mutually unbiased basis measurement system and method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- PENG CHENG LAB
- Filing Date
- 2023-11-30
- Publication Date
- 2026-07-21
Smart Images
Figure CN117639926B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of optical information processing technology, and in particular to a high-dimensional mutual unbiased basis measurement system and method. Background Technology
[0002] In optical information processing, mutually unbiased bases (MUB) measurements are generally considered to be among the most efficient types of measurements for information extraction in Hilbert space. They can be used for calibration of unitary transform linear operating devices and physical layer secure key distribution in optical communication systems. Experimental implementation of MUB measurements requires a series of generalized Fourier transforms to convert the standard basis to its corresponding sets of other mutually unbiased bases.
[0003] Existing methods for achieving mutually unbiased measurements require a large number of 50:50 beam splitters and phase modulators. As the system dimension increases, the number of components increases quadratically, and the area of the optical integrated chip continuously increases, posing challenges to practical implementation.
[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention
[0005] The main objective of this invention is to provide a high-dimensional mutual unbiased basis measurement system and method, which aims to solve the technical problem that mutual unbiased basis measurement requires a large number of components in the prior art.
[0006] To achieve the above objectives, the present invention provides a high-dimensional mutually unbiased basis measurement system, the high-dimensional mutually unbiased basis measurement system comprising: at least two phase modulation modules and a multi-beam interferometry module; The at least two phase modulation modules are respectively connected to the multi-beam interferometry module, and the number of phase modulation modules is the same as the system dimension of the high-dimensional mutually unbiased measurement system. The phase modulation module is used to modulate the phase of the incident beam to obtain a modulated beam, and to transmit the modulated beam to the multi-beam interference module; The multi-beam interferometry module is used to interfere with each of the received modulated beams based on the principles of multimode interferometry and self-image to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to realize mutual unbiased basis measurement.
[0007] Optionally, the multi-beam interference module is an N×N port multi-port beam splitter; The multi-beam interference module includes: N input waveguides, a multimode waveguide, and N output waveguides, where N is an integer greater than or equal to 2; The input waveguide is connected to the phase modulation module, and the multimode waveguide is connected to both the input waveguide and the output waveguide.
[0008] Optionally, the multimode waveguide supports multiple optical field modes; The input waveguide is used to couple the modulated beam into the multimode waveguide; During the transmission of the modulated beam in the multimode waveguide, the phase of the optical field mode of the modulated beam changes, forming interference, so that the multimode waveguide periodically presents the self-image of the modulated beam. The output waveguide is used to output the self-image.
[0009] Optionally, the standard Fourier transform matrix is determined based on the self-image in each of the output waveguides; The operation of determining the standard Fourier transform matrix includes: The standard discrete Fourier transform matrix corresponding to the incident beam is determined based on the self-image in each of the output waveguides. Other generalized discrete Fourier transform matrices of the incident beam are obtained by performing diagonal unitary and transpose transformations on the standard discrete Fourier transform matrix; the standard Fourier transform matrix includes the generalized discrete Fourier transform matrix.
[0010] Optionally, in the multimode waveguide, the position where the first N-fold image appears is... ; in, , The refractive index of the waveguide core layer, The incident light wavelength, , The cladding refractive index, For the multimode waveguide width, Mode polarization factor; The location of the first N-fold image is optimized based on the width and length of the multimode waveguide.
[0011] Optionally, the input waveguide includes an input gradient region on the side closest to the multimode waveguide; The output waveguide includes an output gradient region on the side closest to the multimode waveguide. The input gradient region is used to improve the coupling effect of the light beam from the waveguide to the multimode waveguide. The output gradient region is used to improve the coupling effect of the multimode waveguide beam.
[0012] Optionally, the phase modulation module is also used to perform phase modulation on the incident beam to achieve switching between different mutually unbiased bases.
[0013] Optionally, the multi-beam interference module is based on lithium niobate or silicon-based integration.
[0014] Furthermore, to achieve the above objectives, this invention also proposes a high-dimensional mutually unbiased basis measurement method, which is applied to the high-dimensional mutually unbiased basis measurement system described above, and the method includes: The phase modulation module modulates the phase of the incident beam to obtain a modulated beam, and then transmits the modulated beam to the multi-beam interference module. The multi-beam interferometry module, based on the principles of multimode interferometry and self-image, interferes with each of the received modulated beams to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to achieve mutual unbiased basis measurements.
[0015] Optionally, the multi-beam interferometry module, based on the principles of multimode interferometry and self-image, performs interference on each of the received modulated beams to obtain a standard Fourier transform matrix, including the following steps: The input waveguide couples the modulated beam into the multimode waveguide; wherein, during the transmission of the modulated beam in the multimode waveguide, the phase of the optical field mode of the modulated beam changes, forming interference, so that the multimode waveguide periodically presents the self-image of the modulated beam; The output waveguide outputs the self-image; The standard Fourier transform matrix is determined based on the self-image in each of the output waveguides; The steps for determining the standard Fourier transform matrix include: The standard discrete Fourier transform matrix corresponding to the incident beam is determined based on the self-image in each of the output waveguides. Other generalized discrete Fourier transform matrices of the incident beam are obtained by performing diagonal unitary and transpose transformations on the standard discrete Fourier transform matrix.
[0016] This invention discloses a high-dimensional basis-free system comprising: at least two phase modulation modules and a multi-beam interferometry module; wherein the at least two phase modulation modules are respectively connected to the multi-beam interferometry module, and the number of phase modulation modules is the same as the system dimension; the phase modulation modules modulate the incident beam to obtain a modulated beam, and transmit the modulated beam to the multi-beam interferometry module; the multi-beam interferometry module, based on the principles of multimode interference and self-image, interferes with each received modulated beam to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to realize mutual basis-free measurement. This invention obtains the standard Fourier transform matrix of the incident beam through phase modulators and a multi-beam interferometry module, providing a foundation for mutual basis-free measurement, significantly reducing the components required for mutual basis-free measurement, and enabling a larger-scale expansion of spatial path coding systems used for optical coding. Attached Figure Description
[0017] Figure 1 A schematic diagram of a scheme for mutual unbiased basis measurement in four-dimensional space; Figure 2 This is a system structure block diagram of the high-dimensional mutual unbiased basis measurement system of the present invention; Figure 3 The system structure block diagram of a four-dimensional mutually unbiased basis measurement system; Figure 4 This is a structural block diagram of a multi-beam interferometry module in one embodiment of the high-dimensional mutual unbiased basis measurement system of the present invention; Figure 5 The image shows the simulation results of the specific propagation of the light field mode in the multi-beam interferometry module. Figure 6 The simulation results of the waveguide light intensity distribution output by the multi-beam interference module are shown in the figure. Figure 7 This is a flowchart illustrating the first embodiment of the high-dimensional mutual unbiased basis measurement system of the present invention.
[0018] Explanation of icon numbers
[0019] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation
[0020] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.
[0021] 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 a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0022] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.
[0023] Furthermore, the use of terms such as "first" and "second" in this invention is for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. Additionally, the technical solutions of the various embodiments can be combined with each other, but only on the basis of being achievable by those skilled in the art. When the combination of technical solutions is contradictory or impossible to implement, the user should consider such a combination of technical solutions to be non-existent and not within the scope of protection claimed by this invention.
[0024] It should be noted that in optical information processing, information extraction relies on measurement, and mutually unbiased bases (MUB) measurements are generally considered the most efficient type of measurement for information extraction in Hilbert spaces. For a complex space of dimension d, when d is a prime number or a prime to the power of m, there are a total of d+1 MUBs. Theoretically, knowing only the measurement probability distributions of d+1 MUBs is sufficient to obtain all the information of the d-dimensional system through state reconstruction algorithms. Therefore, mutually unbiased bases measurements are a very important type of measurement.
[0025] On the other hand, with the introduction of the BB84 protocol, quantum key distribution protocols have achieved a series of research results in theory and experiment, providing an effective physical layer secure communication scheme. Mutual unbiased basis is one of the important factors in ensuring its security. This invention, through the realization of mutual unbiased basis measurement in high-dimensional space, provides important practical application value in improving the coding efficiency of single photons and the security of key distribution in physical layer secure communication systems.
[0026] It should be understood that mutually unbiased bases are an important tool and method in quantum information science and quantum computing. In a vector space, the basis vectors of a mutually unbiased basis satisfy both orthogonality (i.e., their inner product is zero) and mutual normalization. Specifically, for each basis vector in a mutually unbiased basis, the square of its norm is equal to 1 minus the sum of the squares of the norms of the other basis vectors. This ensures that each basis vector in a mutually unbiased basis is orthogonal and normalized relative to the other basis vectors.
[0027] It should be noted that the experimental implementation of mutually unbiased basis measurements requires a series of generalized Fourier transforms to convert the standard basis to its corresponding sets of mutually unbiased bases. In one implementation method, for a high-dimensional optical path coding system, the implementation of the generalized Fourier transform can be divided into two categories. Both implementation schemes are based on Gaussian elimination. Using a 50:50 beam splitter and the corresponding operation matrices of the phase modulator, the off-diagonal elements of the target matrix are eliminated to zero in a specific order. Finally, phase compensation is performed on the diagonal elements of the target matrix, transforming it into a unitary matrix in d-dimensional space. The resulting unitary matrix is the inverse matrix corresponding to the target unitary matrix. By changing the order of the device inputs and outputs and the parameters of the phase modulator, the Fourier transform matrix required for mutually unbiased basis measurements can be obtained.
[0028] like Figure 1 As shown, Figure 1 This is a schematic diagram of an implementation scheme for mutual unbiased basis measurement in four-dimensional space.
[0029] Reference Figure 1 One type of scheme for implementing mutually unbiased basis measurements in four-dimensional space is a triangular structure ( Figure 1 (Left side), another type is rectangular structure ( Figure 1 (Right side). This type of implementation requires a large number of 50:50 beam splitters (black elements in the figure) and phase modulators (gray elements in the figure) connected together. Specifically, for a complex space of dimension d, a total of d(d-1) 50:50 beam splitters and d^2 phase modulators are needed to achieve d+1 sets of mutually unbiased measurements, where d is a prime number or a prime to the power of n.
[0030] It should be noted that for a triangular structure, the line depth, i.e., the number of beam splitters in the longest path, is 2(2d-3); for a rectangular structure, the line depth is 2d. As the system dimension increases, the number of components increases quadratically, and the area of the optical integrated chip continuously increases, posing difficulties for practical implementation.
[0031] As mentioned above, for high-dimensional spatial path coding, when the spatial dimension d is a prime number or a power of n, all MUBs other than the standard basis require the generalized discrete Fourier transform (GFT) for MUB measurement. However, the GFT currently requires at least 2d layers of line depth to implement, and the line depth increases with the system dimension, which is not conducive to large-scale expansion.
[0032] Based on this, the present invention proposes a high-dimensional mutually unbiased basis measurement system, which can be used to directly realize the generalized Fourier transform, thereby realizing multiple sets of high-dimensional mutually unbiased basis measurements.
[0033] The embodiments of the present invention and the following embodiments use four-dimensional space as an example to describe the high-dimensional mutually unbiased basis measurement system of the present invention in detail, but this does not limit the application dimensions of the high-dimensional mutually unbiased basis measurement system of the present invention.
[0034] In specific implementations, the high-dimensional mutually unbiased basis measurement system of the present invention can be applied to an arbitrary d-dimensional spatial path coding system, referring to the method described in the embodiments of the present invention. Here, d is a prime number or a prime number to the power of n, and n is a positive integer, such as two-dimensional, three-dimensional, four-dimensional, five-dimensional, or other dimensions.
[0035] To address the problem that the number of components required for mutual unbiased basis measurement schemes increases exponentially with the increase of system dimension, resulting in a large number of components being needed for mutual unbiased basis measurement, the first embodiment of the high-dimensional mutual unbiased basis measurement system of the present invention is proposed.
[0036] Reference Figure 2 , Figure 2 This is a system structure block diagram of the high-dimensional mutual unbiased basis measurement system of the present invention.
[0037] like Figure 2 As shown, the high-dimensional mutually unbiased basis measurement system of this invention mainly comprises two parts: a phase modulation module (labeled 1 in the figure) and a multi-beam interferometry module (labeled 2 in the figure). By modulating the phase of incident beams from different paths through the phase modulation module, switching between unbiased bases can be achieved; by using the multi-beam interferometry module, a standard Fourier transform can be performed, thereby enabling the measurement of mutually unbiased bases and thus extracting the optical information of the incident beam.
[0038] It is understood that the aforementioned phase modulation module is a module that can be used to modulate the phase of an incident beam. Specifically, it can be a liquid crystal, a grating, an optical waveguide, a phase delay plate, or other components capable of achieving phase modulation. Similarly, the aforementioned multi-beam interference module is a module that can be used to perform multimode interference on an incident beam. Specifically, it can be a multimode interference coupler, a grating, a waveguide, a spatial light modulator, or other components used to achieve multimode interference.
[0039] It should be noted that, in this embodiment of the invention, the number of phase modulation modules is the same as the dimension d of the spatial path coding system.
[0040] As can be understood, a phase modulation module is a module capable of modulating the phase of an incident beam. Through the phase modulation module, the phase of the incident beam can be changed, thereby achieving switching between different mutually unbiased bases. That is, the phase modulation module is used to modulate the phase of the incident beam to obtain a modulated beam, and then transmits the modulated beam to the multi-beam interference module.
[0041] It should be noted that the phase modulation module can be connected to the multi-beam interference module. This connection can be understood as the incident beam, after being adjusted by the phase modulation module, being directed into the multi-beam interference module.
[0042] It needs to be explained that adjusting the incident beam using a phase modulator is equivalent to transforming the incident beam into a modulated beam with different optical field modes. Specifically, an optical field mode refers to the distribution and propagation characteristics of light in the transmission medium. When the phase of the incident beam changes, the positions of the peaks and troughs also change accordingly, which leads to a change in the distribution of light and thus alters the optical field mode.
[0043] It should be understood that the optical field mode can be represented as a linear combination of a set of basis functions, where each basis function can correspond to an unbiased basis. The unbiased basis can represent the component of the optical field in the direction of the basis vector, thereby realizing the switching of mutual unbiased bases through a phase modulator.
[0044] It should be noted that when modulated beams of different light field modes propagate forward in the multi-beam interference module, the phases of each light field mode will change, thereby forming interference. This allows the propagation of the beam to periodically present one or more images of the light field, that is, a self-image effect occurs. This effect is the basic principle for realizing Fourier transform in this invention.
[0045] It should be noted that the self-imaging effect, also known as the Zeeman effect, is a special interference phenomenon in optics. It describes how a plane wave, when passing through a periodic lens or grating, exhibits a complete or partial self-replication at a certain distance. Specifically, when a modulated beam is incident on a multi-beam interferometer, beams of different optical modes interfere with each other at different positions with different phases, resulting in an interference image of the incident modulated beam after propagating a certain distance. This mutual interference is called multimode interference, and the generated interference image is the self-image of the modulated beam. The location and shape of the self-image can be determined based on the geometric parameters of the multi-beam interferometer and the wavelength of the incident modulated beam.
[0046] It should be explained that by adjusting the design parameters of the multi-beam interferometry module, the self-images of different frequencies in the modulated beam can be distributed at different positions, thereby achieving frequency domain decomposition of the optical signal of the modulated beam incident on the multi-beam interferometry module based on the self-image effect. The standard Fourier transform matrix corresponding to the modulated beam can be determined through the output of the multi-beam interferometry module. That is, the multi-beam interferometry module is used to interfere with each of the received modulated beams based on the principles of multimode interference and self-image to obtain the standard Fourier transform matrix; the standard Fourier transform matrix is used to achieve mutually unbiased basis measurements.
[0047] In one implementation, taking a spatial path coding system with a system dimension d=4 as an example, such as... Figure 3 As shown, Figure 3 This is a system block diagram of a four-dimensional mutually unbiased basis measurement system.
[0048] In the diagram, 201, 202, 203, and 204 are phase modulation modules, and 205 is a multi-beam interference module.
[0049] It should be noted that for spatial path coding systems of other dimensions, mutual unbiased basis measurement of the spatial path coding system can be completed simply by increasing the number of phase modulators according to the number of incident beams. The specific number of phase modulators is d, that is, the number of phase modulators, the number of incident beams and the dimension of the spatial path coding system are the same.
[0050] It should be explained that the design concept of the multi-beam interferometry module is based on multimode interference and self-mapping effect. Through the multi-beam interferometry module, multimode interference can be performed on the beams incident from the phase modulator, thereby obtaining the standard Fourier transform matrix. Through the standard Fourier transform matrix, mutual unbiased basis measurement can be achieved.
[0051] It should be noted that the aforementioned spatial path coding system is an optical coding technology that uses optical devices and complex optical paths to encode data, thereby writing and reading multiple data bits simultaneously to achieve high-density, large-capacity data storage and transmission.
[0052] It should be understood that in a spatial path coding system, the original beam can be split by a beam splitter, and then each incident beam obtained by the split can be emitted into a phase modulation module, thereby enabling a high-dimensional mutual unbiased basis measurement system to perform mutual unbiased basis measurements on each incident beam.
[0053] It should be noted that for a d-dimensional Hilbert space, the Fourier transform is the key structure for achieving mutually unbiased bases. The Fourier basis obtained after the Fourier transform, together with the standard basis {0, 1…d-1}, forms a pair of mutually unbiased bases. Other sets of mutually unbiased bases require generalized discrete Fourier transform matrix operations, any of which can be obtained by performing diagonal and transpose transformations on the standard discrete Fourier transform matrix whose first row and first column elements are 1. In this invention, the standard discrete Fourier transform matrix of the incident beam can be obtained through a multi-beam interference module. By adding different phases to different spatial encoding paths of the incident light through a phase modulator, a diagonal transformation of the standard discrete Fourier transform matrix can be achieved.
[0054] In one implementation, the multi-beam interference module of the present invention can be implemented based on a lithium niobate integrated platform, or it can be implemented based on a silicon-based or other integrated platform. The embodiments of the present invention do not limit this.
[0055] It is understood that the standard discrete Fourier transform matrix can be directly realized through the multi-beam interferometer module of the present invention. By adding a phase modulator in front of the multi-beam interferometer module, the standard discrete Fourier transform matrix can be converted into other generalized discrete Fourier transforms, thereby realizing multiple sets of high-dimensional mutual unbiased basis measurements.
[0056] Compared to traditional solutions, the high-dimensional mutual basis-free measurement system of this invention eliminates the need for multiple sets of 50:50 beam splitters and phase modulators, resulting in a simpler overall structure and better stability. Furthermore, the line depth of this invention does not increase with the system dimension, making it easier to extend to higher dimensions. Additionally, the key component of this invention, the multi-beam interferometry module, is compatible with existing optical integration technologies and can be widely applied on a large scale to physical layer secure communication systems, state tomography and process tomography techniques, and other fundamental physical theories such as noncommutativity.
[0057] This embodiment of the high-dimensional basis-free system includes: at least two phase modulation modules and a multi-beam interferometry module; wherein, at least two phase modulation modules are respectively connected to the multi-beam interferometry module, and the number of phase modulation modules is the same as the system dimension; the phase modulation modules modulate the incident beam to obtain a modulated beam, and transmit the modulated beam to the multi-beam interferometry module; the multi-beam interferometry module, based on the principles of multimode interference and self-image, interferes with each received modulated beam to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to realize mutual basis-free measurement. This invention obtains the standard Fourier transform matrix of the incident beam through phase modulators and a multi-beam interferometry module, providing a foundation for mutual basis-free measurement, significantly reducing the components required for mutual basis-free measurement, and enabling a larger-scale expansion of the spatial path coding system used for optical coding.
[0058] refer to Figure 4 , Figure 4 This is a structural block diagram of a multi-beam interferometry module in one embodiment of the high-dimensional mutual unbiased basis measurement system of the present invention.
[0059] Based on the first embodiment described above, in this embodiment, the present invention will be described in detail using a multi-mode interference (MMI) as the multi-beam interference module of the present invention.
[0060] It should be understood that multimode interference couplers have advantages such as compact structure, wavelength insensitivity, low loss, and ease of manufacturing, and are currently widely used in devices such as wavelength division multiplexers, optical switches, and Mach-Zehnder interferometers.
[0061] Specifically, the multi-beam interference module of the present invention is an N×N port multi-port beam splitter; The input waveguide is connected to the phase modulation module, and the multimode waveguide is connected to both the input waveguide and the output waveguide.
[0062] The multi-beam interference module includes N input waveguides, a multimode waveguide, and N output waveguides, where N is an integer greater than or equal to 2.
[0063] It should be noted that the number of input waveguides and the number of output waveguides are the same, and this number N is the same as the dimension d of the spatial path coding system.
[0064] like Figure 4 As shown, Figure 4 This is a schematic diagram of a multi-beam interferometry module in a four-dimensional spatial path coding system. The multi-beam interferometry module consists of an input waveguide ( Figure 4 It consists of 206, 207, 208, 209, multimode waveguide (210) and output waveguide (211, 212, 213, 214).
[0065] It should be noted that the modulated beam emitted by the phase modulator is coupled to the multimode waveguide via the input waveguide. To better couple the beam in the input waveguide into the multimode waveguide, a standard region and a tapered input gradient region are provided in the input waveguide. The input gradient region is located on the side of the input waveguide closest to the multimode waveguide, and the length of the tapered region is L. taper The width of the cone region is W taper The waveguide width in the standard region is W. WG The waveguide spacing between each cone region is gap.
[0066] Similarly, to better couple the beam from the multimode waveguide to the standard-sized output waveguide, the output waveguide includes a standard region and a tapered output transition region. The tapered output transition region is located on the side of the output waveguide closest to the multimode waveguide, and its tapered length is L. taper The width of the cone region is W taper The waveguide width in the standard region is W. WG The waveguide spacing between each cone region is gap.
[0067] It should be noted that the width of the multimode waveguide region is W. MMI It can support multiple optical field modes. In a multimode waveguide, as the optical field propagates forward, the phases of each optical field mode change, forming multimode interference, thus periodically presenting one or more images of the optical field. Depending on different incident conditions, multimode interference can be divided into ordinary interference (N×N), paired interference (2×N), and symmetrical interference (1×N). This invention mainly uses ordinary interference with N-port input and N-port output (i.e., N×N).
[0068] It should be noted that in a multimode waveguide, the position where the first N-image appears is... ,in , The refractive index of the waveguide core layer, The incident light wavelength, , The cladding refractive index, For the multimode waveguide width, is the mode polarization factor.
[0069] As is understandable, the waveguide core layer, which is the core layer in the waveguide responsible for transmitting optical signals, is typically made of a high-refractive-index material, such as silicon or silicon nitride. The waveguide core layer confines the optical signal within itself and allows it to transmit through the waveguide via reflection and refraction.
[0070] It should be understood that the cladding, or cladding layer, is the material located outside the waveguide core. The cladding protects the waveguide core and provides structural support. It is typically made of low-refractive-index materials, such as silicon dioxide (SiO2) or polymers. The cladding protects the waveguide core from external physical or chemical damage. Simultaneously, because the refractive index of the cladding material is generally lower than that of the waveguide core, it can influence and control the optical field mode distribution within the waveguide. By appropriately designing the cladding thickness and refractive index, the mode-switching characteristics and optical coupling efficiency of the waveguide device can be altered, thereby achieving the modulation of optical signals.
[0071] It should be noted that the position of the output waveguide is set according to the location of the first N-fold self-image, enabling the output waveguide to output the N-fold self-image. Based on the N-fold self-images of each optical field mode, the Discrete Fourier Transform (DFT) matrix can be determined. By adding different phases on different control encoding paths through the phase modulation module, the diagonal unitary matrix transformation of the DFT matrix is achieved. By changing the label of the output waveguide, the transpose matrix transformation of the DFT matrix can be achieved. By performing diagonal unitary and transpose matrix transformations on the standard DFT with elements of 1 in the first row and first column, the generalized DFT operation is performed on each set of mutually unbiased bases.
[0072] It should be understood that the generalized discrete Fourier transform can include the standard discrete Fourier transform matrix, which includes the generalized discrete Fourier transform matrix.
[0073] It should be noted that in traditional designs, the Fourier transform of spatial path coding multibeams requires the use of at least 2d layers of 2×2 beam splitters and phase modulators. The solution of this invention does not require the addition of a large number of beam splitters and phase modulators when the system dimension increases, thus providing basic support for the expansion of spatial path coding systems.
[0074] In the high-dimensional mutually unbiased basis measurement system of this invention, the multi-beam interferometry module is an N×N port multi-port beam splitter, where N is an integer greater than or equal to 2. The multi-beam interferometry module includes N input waveguides, a multimode waveguide, and N output waveguides. The input waveguides are connected to the phase modulation module, and the multimode waveguides are connected to both the input and output waveguides. Since the multi-beam interferometry module includes N input waveguides, a multimode waveguide, and N output waveguides, multimode interference of light is achieved through the multimode waveguides, and the standard Fourier transform matrix is determined based on the self-image effect, providing a foundation for mutually unbiased basis measurement in high-dimensional spatial path coding systems. Compared to existing solutions, this invention eliminates the need for multiple sets of 50:50 beam splitters and phase modulators, resulting in a simpler overall structure, better stability, and a line depth that does not increase with system dimensionality, making it easier to extend to higher dimensions. Furthermore, the key component of this invention—the equalization beam splitter (i.e., the multi-beam interference module)—is compatible with existing optical integration technology and can be widely applied on a large scale to physical layer secure communication systems, state tomography and process tomography techniques, as well as other research on fundamental physical theories such as noncommutativity.
[0075] Based on the above embodiments of the high-dimensional mutually unbiased basis measurement system of the present invention, a third embodiment of the high-dimensional mutually unbiased basis measurement system of the present invention is proposed.
[0076] In this embodiment, in order to optimize the performance of the high-dimensional mutually unbiased basis measurement system, the structural parameters of the multi-beam interferometry module are optimized by simulation based on the theoretical position of the first N-fold image.
[0077] In one implementation, a four-port multimode interference coupler based on a lithium niobate optical integration platform is taken as an example. Specifically, due to the width W of the multimode waveguide... MMI The width of the multimode waveguide directly determines whether the optical field intensity distribution of the output waveguide is uniform. Therefore, the width of the multimode waveguide directly determines the quality of the Fourier transform operation. The multimode waveguide width W obtained through optimization... MMI The location of the first quadruple image can be calculated, which also determines the length L of the multimode waveguide. MMI After determining the length and width of the multimode waveguide, the cone parameters (i.e., the parameters of the gradient region) of the output and input waveguides are optimized to reduce the optical field loss of the multi-beam interference module, which in turn reduces the loss of the Fourier transform operation.
[0078] In one implementation, the optimized values of each parameter are shown in the table below:
[0079] It should be noted that under these numerical conditions, the specific distribution of multimode multiwaves can be obtained using a Finite-Difference Time-Domain (FDTD) module. For example... Figure 5 As shown, Figure 5 The figure shows the simulation results of the light field mode propagation in the multi-beam interferometer module. As can be seen from the figure, the light incident from the incident waveguide emits multimode interference in the multi-beam interferometer module, allowing the self-image to be evenly distributed in the output waveguide. For a specific incident waveguide, the numerical results for each port can be found in [reference needed]. Figure 6 , Figure 6 The simulation results of the waveguide light intensity distribution output by the multi-beam interference module are shown in the figure.
[0080] Figure 6 Input terminals 1, 2, 3, and 4 represent the four input waveguides of the multi-beam interferometer module. Simulation results show that the insertion loss of this multi-beam interferometer module is less than 0.81 dB. Therefore, this scheme also possesses the characteristic of low insertion loss.
[0081] In one implementation, the standard discrete Fourier transform matrix output by the multi-beam interferometry module can be expressed as: .
[0082] It is understandable that a phase modulator can be used to add phase to each input path separately. , , and Thus, the diagonal matrix of the standard discrete Fourier transform matrix is obtained, which can be represented as: .
[0083] It should be understood that the multi-beam interferometry module enables the transformation of the standard basis M0 onto other mutually unbiased bases. ;in, For U ph The conjugate transpose of . For U BS The conjugate transpose of . For four mutually unbiased bases other than the standard basis in four-dimensional space, add phases {0, 0, 0, 0}, { ... , }, {0, , ,0},{0, ,0, Therefore, by using a phase modulator to adjust the angle of each path, switching between different mutually unbiased bases can be achieved.
[0084] Furthermore, modifications to this solution may include using different integrated materials to achieve multi-port equalized beam splitting devices for different wavelengths, or using various phase adjustment elements, such as doped integrated optical phase modulators, to achieve high-speed switching between MUBs, or improving the device's own fabrication process error tolerance, etc.
[0085] This embodiment optimizes the theoretical position of the first quadruple image by simulating based on the length and width of the multimode waveguide, so that the optical field intensity of the output waveguide is uniformly distributed. By optimizing the parameters of the gradient region, the optical field loss of the multi-beam interference module is reduced.
[0086] Based on the first embodiment of the high-dimensional mutually unbiased basis measurement system of the present invention, a first embodiment of the high-dimensional mutually unbiased basis measurement method of the present invention is proposed, with reference to... Figure 7 , Figure 7 This is a flowchart illustrating the first embodiment of the high-dimensional mutual unbiased basis measurement system of the present invention.
[0087] like Figure 7 As shown, the high-dimensional mutually unbiased basis measurement method proposed in this embodiment of the invention can be applied to the high-dimensional mutually unbiased basis measurement system described above. The method includes: Step S10: The phase modulation module modulates the incident beam to obtain a modulated beam, and then transmits the modulated beam to the multi-beam interference module; Step S20: The multi-beam interferometry module, based on the principles of multimode interferometry and self-image, interferes with each of the received modulated beams to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to realize mutual unbiased basis measurement.
[0088] This embodiment of the high-dimensional basis-free method includes: a phase modulation module modulating the incident beam to obtain a modulated beam, and transmitting the modulated beam to a multi-beam interferometry module; the multi-beam interferometry module, based on the principles of multimode interference and self-image, interfering with each received modulated beam to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to realize mutual basis-free measurement. This invention obtains the standard Fourier transform matrix of the incident beam through a phase modulator and a multi-beam interferometry module, providing a foundation for mutual basis-free measurement, significantly reducing the components required for mutual basis-free measurement, and enabling a larger-scale expansion of spatial path coding systems used for optical coding.
[0089] Furthermore, the multi-beam interference module, based on the principles of multimode interference and self-image, interferes with each of the received modulated beams to obtain a standard Fourier transform matrix, including the following steps: The input waveguide couples the modulated beam into the multimode waveguide; wherein, during the transmission of the modulated beam in the multimode waveguide, the phase of the optical field mode of the modulated beam changes, forming interference, so that the multimode waveguide periodically presents a self-image of the modulated beam; The output waveguide outputs the self-image; The standard Fourier transform matrix is determined based on the self-image in each of the output waveguides; The steps for determining the standard Fourier transform matrix include: The standard discrete Fourier transform matrix corresponding to the incident beam is determined based on the self-image in each of the output waveguides. Other generalized discrete Fourier transform matrices of the incident beam are obtained by performing diagonal unitary and transpose transformations on the standard discrete Fourier transform matrix.
[0090] Furthermore, in the multimode waveguide, the position where the first N-fold image appears is... ; in, , The refractive index of the waveguide core layer, The incident light wavelength, , The cladding refractive index, For the multimode waveguide width, Mode polarization factor; The location of the first N-fold image is optimized based on the width and length of the multimode waveguide.
[0091] Furthermore, the method further includes: the input gradient region improving the coupling effect of the beam from the waveguide to the multimode waveguide; and the output gradient region improving the coupling effect of the beam from the multimode waveguide.
[0092] Furthermore, the method also includes: the phase modulation module performs phase modulation on the incident beam to achieve switching between different mutually unbiased bases.
[0093] Furthermore, the method also includes: the multi-beam interference module is based on lithium niobate or silicon-based integration.
[0094] Other embodiments or specific implementations of the high-dimensional mutual unbiased basis measurement method of the present invention can be referred to the above system embodiments, and will not be repeated here.
[0095] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.
[0096] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.
[0097] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.
[0098] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.
Claims
1. A high-dimensional mutually unbiased basis measurement system, characterized in that, The high-dimensional mutually unbiased basis measurement system includes: at least two phase modulation modules and a multi-beam interferometry module; The at least two phase modulation modules are respectively connected to the multi-beam interferometry module, and the number of phase modulation modules is the same as the system dimension of the high-dimensional mutually unbiased measurement system. The phase modulation module is used to perform phase modulation on the incident beam to achieve switching between different mutually unbiased bases, obtain a modulated beam, and emit the modulated beam to the multi-beam interference module. The multi-beam interferometry module is used to interfere with each of the received modulated beams based on the principles of multimode interferometry and self-image to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to realize mutual unbiased basis measurement.
2. The high-dimensional mutually unbiased basis measurement system as described in claim 1, characterized in that, The multi-beam interference module is an N×N port multi-port beam splitter. The multi-beam interference module includes: N input waveguides, a multimode waveguide, and N output waveguides, where N is an integer greater than or equal to 2; The input waveguide is connected to the phase modulation module, and the multimode waveguide is connected to both the input waveguide and the output waveguide.
3. The high-dimensional mutually unbiased basis measurement system as described in claim 2, characterized in that, The multimode waveguide supports multiple optical field modes; The input waveguide is used to couple the modulated beam into the multimode waveguide; During the transmission of the modulated beam in the multimode waveguide, the phase of the optical field mode of the modulated beam changes, forming interference, so that the multimode waveguide periodically presents the self-image of the modulated beam. The output waveguide is used to output the self-image.
4. The high-dimensional mutually unbiased basis measurement system as described in claim 3, characterized in that, The standard Fourier transform matrix is determined based on the self-image in each of the output waveguides; The operation of determining the standard Fourier transform matrix includes: The standard discrete Fourier transform matrix corresponding to the incident beam is determined based on the self-image in each of the output waveguides. Other generalized discrete Fourier transform matrices of the incident beam are obtained by performing diagonal unitary and transpose transformations on the standard discrete Fourier transform matrix; the standard Fourier transform matrix includes the generalized discrete Fourier transform matrix.
5. The mutual unbiased basis measurement system as described in claim 3, characterized in that, In the multimode waveguide, the position where the first N-fold image appears is: ; in, , The refractive index of the waveguide core layer, The incident light wavelength, , The cladding refractive index, For the multimode waveguide width, Mode polarization factor; The location of the first N-fold image is optimized based on the width and length of the multimode waveguide.
6. The high-dimensional mutually unbiased basis measurement system as described in claim 2, characterized in that, The input waveguide includes an input gradient region on the side closest to the multimode waveguide. The output waveguide includes an output gradient region on the side closest to the multimode waveguide. The input gradient region is used to improve the coupling effect of the light beam from the input waveguide to the multimode waveguide. The output gradient region is used to improve the coupling effect of the multimode waveguide beam.
7. The high-dimensional mutually unbiased basis measurement system as described in any one of claims 1-5, characterized in that, The multi-beam interference module is based on lithium niobate or silicon-based integration.
8. A method for measuring high-dimensional mutually unbiased bases, characterized in that, The method is applied to the high-dimensional mutually unbiased basis measurement system as described in any one of claims 1-7, and the method includes: The phase modulation module modulates the incident beam to achieve switching between different mutually unbiased bases, obtains a modulated beam, and transmits the modulated beam to the multi-beam interference module. The multi-beam interferometry module, based on the principles of multimode interferometry and self-image, interferes with each of the received modulated beams to obtain a standard Fourier transform matrix; the standard Fourier transform matrix is used to achieve mutual unbiased basis measurements.
9. The high-dimensional mutually unbiased basis measurement method as described in claim 8, characterized in that, The multi-beam interference module is an N×N port multi-port beam splitter. The multi-beam interference module includes: N input waveguides, a multimode waveguide, and N output waveguides, where N is an integer greater than or equal to 2; The multi-beam interferometry module, based on the principles of multimode interferometry and self-image, performs interference on each of the received modulated beams to obtain a standard Fourier transform matrix, including the following steps: The input waveguide couples the modulated beam into the multimode waveguide; wherein, during the transmission of the modulated beam in the multimode waveguide, the phase of the optical field mode of the modulated beam changes, forming interference, so that the multimode waveguide periodically presents the self-image of the modulated beam; The output waveguide outputs the self-image; The standard Fourier transform matrix is determined based on the self-image in each of the output waveguides; The steps for determining the standard Fourier transform matrix include: The standard discrete Fourier transform matrix corresponding to the incident beam is determined based on the self-image in each of the output waveguides. Other generalized discrete Fourier transform matrices of the incident beam are obtained by performing diagonal unitary and transpose transformations on the standard discrete Fourier transform matrix; the standard Fourier transform matrix includes the generalized discrete Fourier transform matrix.