CN117391211A - Multi-photon state chromatography method based on linear optical network - Google Patents
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Abstract
The embodiment of the application provides a multi-photon state chromatography method based on a linear optical network, which comprises the following steps: acquiring an optical signal to be detected; the quantum system corresponding to the optical signal to be detected comprises a plurality of polarization entangled photon pairs, and the quantum state of the quantum system is a pure state or a mixed state; inputting an optical signal to be detected into a linear optical network, and performing quantum operation on a plurality of polarization entangled photon pairs by utilizing an optical path corresponding to a set of positive operator measurement operators to obtain an output quantum state corresponding to the linear optical network; acquiring measurement results of optical paths by using a photon number resolvable detector, and carrying out probability statistics on the measurement results of a plurality of optical paths obtained by measuring the optical signals to be measured for target times to obtain a density matrix corresponding to a quantum state of the quantum system; the density matrix is used to represent either pure or mixed states. According to the method, the function of measuring the quantum state based on a group of positive operator measurement operators is realized by using the optical path to carry out quantum operation, and the efficiency of multi-photon state chromatography can be improved.
Description
Technical Field
The application relates to the technical field of quantum measurement, in particular to a multiphoton state chromatography method based on a linear optical network.
Background
Quantum state chromatography (quantum state tomography, QST), also known as quantum state prediction (quantum state estimation, QSE), is mainly used for the reconstruction of states in quantum systems. In conventional classical physics, information about an object can be obtained by directly measuring its properties. However, in quantum physics, measuring a certain property of a quantum system can result in the quantum state collapsing onto a certain defined state, due to the superposition nature of the quantum states. Thus, in order to fully understand and describe a quantum system, it is necessary to measure and analyze multiple properties.
Quantum state chromatography techniques allow for accurate measurement and analysis of quantum states through the use of various quantum measurement methods and techniques, such as photon detectors, interferometers, optics, and the like. It may provide detailed information about the different parameters and characteristics of the quantum system, such as the amplitude and phase distribution of the state vector, the elements of the density matrix, etc. By measuring and analyzing these parameters, more information about the quantum system can be obtained, such as its entanglement properties, coherence, form of quantum superposition, etc.
Currently, techniques have been disclosed that can be based on general purpose computers using projection measurements or positive definite operator measurements for quantum state reconstruction. However, the speed of quantum state measurements using these techniques is slow. For example, if an 8bit quantum state needs to be reconstructed, data acquisition for tens of hours and numerical calculation for nearly one week are required, and the use requirements of modern quantum calculation or quantum communication can not be met far.
Therefore, a method for improving the quantum state chromatography efficiency is required to be proposed in practical application.
Disclosure of Invention
The application provides a multi-photon state chromatography method based on a linear optical network, which can improve the efficiency of quantum state chromatography.
The technical scheme adopted for solving the technical problems is to provide a multi-photon state chromatography method based on a linear optical network, which comprises the following steps: acquiring an optical signal to be detected; the quantum system corresponding to the optical signal to be detected comprises a plurality of polarization entangled photon pairs, and the quantum state of the quantum system is a pure state or a mixed state; inputting an optical signal to be detected into a linear optical network, and performing quantum operation on a plurality of polarization entangled photon pairs by utilizing an optical path corresponding to a set of positive operator measurement operators to obtain an output quantum state corresponding to the linear optical network; the quantum operation realizes the function of measuring the quantum state based on a group of positive operator measuring operators, the optical path is realized by a polarization beam splitter and a glass slide in a linear optical network, and the output quantum state is expressed as the projection result of the quantum state on the group of positive operator measuring operators; acquiring measurement results of optical paths by using a photon number resolvable detector, and carrying out probability statistics on the measurement results of a plurality of optical paths obtained by measuring the optical signals to be measured for target times to obtain a density matrix corresponding to a quantum state of the quantum system; the density matrix is used to represent either pure or mixed states.
Therefore, the quantum operation is carried out by using the optical path to realize the function of measuring the quantum state based on a group of positive operator measuring operators, and the efficiency of multi-photon state chromatography can be improved.
In one possible implementation, the number of input ports of the linear optical network is determined according to the following formula:
wherein R is N，M Representing the number of input ports of the linear optical network, N represents the number of photons comprised by the plurality of polarization entangled photon pairs, and M represents the number of polarization modes comprised by the plurality of polarization entangled photon pairs.
In one possible implementation, the number of output ports of the linear optical network is equal to the number of positive operator measurement operators comprised by the set of positive operator measurement operators, one of the output ports being in one-to-one correspondence with one of the set of positive operator measurement operators, the number of positive operator measurement operators being determined in dependence on the number of polarization modes comprised by the plurality of polarization entangled photon pairs.
In a possible implementation manner, according to the method of claim 1, probability statistics is performed on measurement results of a plurality of optical paths obtained by measuring an optical signal to be measured by a target number of times, including: based on projection results respectively corresponding to the plurality of output quantum states, counting the output times of each photon in the plurality of polarization entangled photon pairs from each output port of the linear optical network to obtain statistical data; calculating probability distribution corresponding to each output port of the linear optical network based on the statistical data; and solving a density matrix corresponding to the quantum state of the quantum system based on the probability distribution.
In one possible implementation, a set of positive operator measurement operators is represented by the following formula:
|π 1 >＝|H>，
wherein pi 1 、π 2 、π 3 And pi 4 One positive operator measurement operator, H, representing a set of positive operator measurement operators, respectively>And |V>Each representing a polarization mode of a plurality of polarization entangled photons.
In one possible implementation, acquiring the optical signal to be measured includes: preparing single photons by using a spontaneous parametric down-conversion technique; and carrying out optical interference and modulation on the plurality of single photons to obtain a plurality of polarization entangled photon pairs so as to obtain an optical signal to be detected.
In one possible implementation, inputting an optical signal to be measured into a linear optical network includes: receiving an optical signal to be detected by using an optical fiber coupling device; and processing the optical signal to be detected by using the optical fiber polarization maintaining device and the polarization operation device.
In one possible implementation, obtaining a measurement of an optical path with a photon-number-resolvable detector includes: processing the optical signal obtained after quantum operation by using an optical fiber polarization maintaining device and a polarization operating device; outputting the processed optical signal by using an optical fiber coupler; and receiving the optical signal obtained after the processing by using a photon number distinguishable detector so as to obtain the measurement result of the optical path.
In one possible implementation, the structure and configuration of the linear optical network remains unchanged during the multi-photon state chromatography.
In one possible implementation, the operating environment of the linear optical network includes a set of temperatures of 25-27 ℃ and one standard atmospheric pressure.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a multi-photon state chromatography method based on a linear optical network according to an embodiment of the present application;
fig. 2 is a schematic structural diagram of a linear optical network according to an embodiment of the present application;
FIG. 3 is a flow chart of a multi-photon state chromatography method based on a linear optical network according to an embodiment of the present application;
fig. 4 is a schematic structural diagram of an optical path according to an embodiment of the present application.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
Quantum state chromatography is a technique for measuring and analyzing quantum states. In quantum physics, a quantum state is a mathematical expression describing the state of a quantum system. Quantum state chromatography aims to reveal the properties and behaviour of quantum systems by measuring and analysing different parameters of the quantum states.
Quantum state chromatography is mainly used for reconstructing states in a quantum system. Quantum state reconstruction refers to the process of recovering the original quantum state by a series of measurement and data processing methods. In quantum mechanics, the quantum states may be represented by a vector or density matrix. The goal of the quantum state reconstruction is to extrapolate the representation of the original quantum state from the experimentally measured data.
There are a number of methods and techniques currently available for measuring and analyzing quantum states, common quantum state chromatography techniques including:
based on the quantum state chromatography technology of a balanced homodyne detector (homode), a quasi-probability distribution Winger function of the quantum state can be approximately estimated by using the homode, and the function is a function used for describing the quantum state in the field of quantum optics. Each measurement of Homodyne can obtain a quantum state orthogonal operator measurement value, and the measurement under a large number of identical conditions can obtain probability distribution of a group of orthogonal operator measurement values. And then, the relative phase of the signal light is scanned from 0 to pi to obtain all information of quantum states needing to be reconstructed, and finally, the Wigner function can be reversely obtained by utilizing the probability distribution through a numerical processing method.
The other is to use projection measurement to perform quantum state chromatography, the basic principle is to prepare a group of orthogonal ground states (or called observation states), and internal elements meet the requirement of mutual orthogonality, usually { |alpha 1 >，|α 2 >，...|α n >Such a matrix is then represented, and the quantum states are then projected onto the respective ground states of the measurement basis by interacting with the measurement basis such that there is a certain probability of the quantum states. For example: quantum state |psi>Projection to the ground state |alpha n >The probability of success of projection of (2) can be used<α n |ψ>| 2 To show that by a large number of measurements, a set of |ψ can be obtained as well>Projected at { |alpha 1 >，|α 2 >，...|α n >Probability distribution over each element, thenThe quantum state |psi can be obtained through numerical calculation>Is a density matrix of (a) for a plurality of optical elements.
Yet another approach is to use positive operator-measured (posiveoperator-measured) to implement quantum state chromatography. Positive definite operator measurement is a generalized measurement method in quantum mechanics, and is generally carried out by { pi } n And is represented by a set of measurement operators. Compared with projection measurement, the quantum system is described in a wider range, because the internal elements do not need to meet the requirement of orthogonality, only the operator is hermite and the sum is equal operator sigma n Π n =1. Currently, techniques have been disclosed that can be based on general purpose computers using projection measurements or positive definite operator measurements for quantum state reconstruction.
However, the speed of quantum state measurements using these techniques is slow. For example, if an 8bit quantum state needs to be reconstructed, data acquisition for tens of hours and numerical calculation for nearly one week are required, and the use requirements of modern quantum calculation or quantum communication can not be met far.
Therefore, a method for improving the quantum state chromatography efficiency is required to be proposed in practical application.
In view of this, an embodiment of the present application proposes a multi-photon state chromatography method based on a linear optical network, by preparing a quantum state including a plurality of polarization entangled photon pairs, and performing quantum operations on the plurality of polarization entangled photon pairs using an optical path in the linear optical network, so as to implement a function of measuring the quantum state based on a set of positive definite operator measurement operators, and finally, obtaining a density matrix corresponding to the quantum state by performing statistical analysis on the results of the plurality of measurements. Therefore, the process of measuring the quantum state based on a set of positive operator measuring operators, which is usually realized by a computer, is converted into an optical path consisting of optical devices to be realized, and the efficiency of quantum state chromatography can be improved.
Referring to fig. 1, a flow chart of a multi-photon state chromatography method based on a linear optical network is provided in an embodiment of the present application. The scheme proposed in the present application will be schematically described with reference to steps S101-S104 in fig. 1 in combination with a complete specific application example. This application example describes a specific process of multiphoton state chromatography.
Step S101, two-photon non state of two polarization modes is prepared.
In this embodiment, the quantum state is composed of two polarization entangled two photons of two polarization modes, wherein the two polarization entangled photons are in the NOON state.
In quantum optics, the NOON state is a multi-entangled state of quantum mechanics. This represents the superposition of N photons in polarization mode a with 0 photons in polarization mode b and vice versa. The two-photon NOON state for two polarization modes can be formulated as:
where H and V represent the polarization modes of the photons and φ represents the relative phases of the photons. As can be seen from equation (1), the quantum state consists of two polarization modes and two photons.
In one implementation, a process for preparing a quantum state includes:
first, single photons are prepared using a spontaneous parametric down-conversion method. The principle is that the high-frequency photons interact with the nonlinear medium to split into two low-frequency photons, so that the preparation of single photons is realized. As this technology is now substantially mature, it is not further elucidated in the present invention.
Further, a two-photon HOM interference method may be used to prepare the two-photon non state of the two polarization modes in formula (1), which specifically includes the following steps:
(1) Two low frequency photons are modulated onto mutually perpendicular polarization modes, i.e. one photon has a polarization mode of |H >, and the other photon has a polarization mode of |V >.
(2) 2 paths of photons with mutually perpendicular polarizations are combined into one path through the polarization beam splitter, and the two photons are guaranteed to reach the polarization beam splitter in the same time, the same spatial mode and the same frequency mode.
(3) A half-wave plate with an optical axis adjusted to-22.5 degrees is placed at an output port of the polarization beam splitter, so that the preparation of the two-photon NOON state in two polarization modes is realized.
As shown in formula (1), the two-photon NOON state of the two polarization modes is a pure state, namely a quantum state |ψ> NOON Is a defined state.
And S102, constructing a linear optical network, and measuring the quantum state by using the linear optical network.
In this embodiment, positive-operator measurement (POVM) is used to achieve quantum state chromatography.
Specifically, a set of positive operator measurement operators required for positive operator measurement is designed based on the polarization mode of the quantum state. And then an optical path is built in the linear optical network to realize the measurement process of the positive operator.
In quantum mechanics, positive operator measurement operator (positive operator) refers to a self-contained (Hermitian) operator, namely Hermitian, whose eigenvalues are all non-negative real numbers. Positive operator measurement operators may be used to describe certain properties of physical quantities, such as probability, energy, density, etc. Whereas the POVM is a set of positive operator measurement operators (positive operator), the sum of which is equal to the unit operator.
Fig. 2 is a schematic structural diagram of a linear optical network according to an embodiment of the present application. As shown in fig. 2, the linear optical network includes a photon input coupling module 210, a photon operation module 220, and a photon output module 230.
The photon input coupling module 210 mainly includes an optical fiber coupling input device, an optical fiber polarization maintaining device, and a polarization operation device, and is configured to receive an optical signal corresponding to a quantum state, and perform a preprocessing operation on the optical signal corresponding to the quantum state to eliminate optical signal interference.
The photon manipulation module 220 includes an optical path that is constructed at least by optics such as polarizing beam splitters and slides. The optical path is used to implement the measurement function of the selected set of positive operators. Specifically, the photon operation module 220 performs quantum operation on the two photons with two polarization modes prepared in step S101, so as to obtain an output quantum state corresponding to the linear optical network. The output quantum states represent the projected result of the quantum states on a set of positive operator measurement operators.
The photon output module 230 mainly includes an optical fiber coupling input device, an optical fiber polarization maintaining device and a polarization operation device, and is configured to receive an optical signal associated with an output quantum state corresponding to the linear optical network, and perform post-operation processing on the optical signal, for example, further eliminate optical signal interference, that is, output optical signal of the linear optical network. It can be understood that the output optical signal of the linear optical network corresponds to an output quantum state obtained by quantum operating the quantum state through an optical path.
And step S103, carrying out probability statistics based on measurement results of a plurality of optical paths obtained by measuring the quantum state for a plurality of times, and reconstructing the quantum state.
In this embodiment, a multiphoton number distinguishable detector is used to receive the output optical signal of the linear optical network and detect photons in the output optical signal.
And carrying out probability statistics based on measurement results of a plurality of optical paths obtained by measuring the quantum state for a plurality of times, carrying out quantum state reconstruction based on measurement statistics data, and analyzing the performance of the quantum state according to the reconstructed result to determine the quantum state as described in the formula (1).
Next, based on the content analyzed in fig. 1-2 above, a multi-photon state chromatography method based on a linear optical network according to an embodiment of the present application will be described in detail.
Fig. 3 shows a flowchart of a multi-photon state chromatography method based on a linear optical network according to an embodiment of the present application. As shown in fig. 3, the multiphoton state chromatography method mainly includes the following steps:
step S301, an optical signal to be detected is obtained, and a quantum system corresponding to the optical signal to be detected includes a plurality of polarization entangled photon pairs. In this embodiment, the optical signal to be measured corresponds to a closed quantum system, and the quantum system refers to a system composed of a plurality of quantum particles, such as a plurality of photons.
In one implementation, a spontaneous parametric down-conversion technique is used to prepare single photons, and then a plurality of single photons are subjected to optical operations such as optical interference and modulation, so as to obtain a plurality of polarization entangled photon pairs. And acquiring an optical signal to be detected based on a quantum system formed by a plurality of polarization entangled photon pairs. And predicting the quantum state of the quantum system corresponding to the optical signal, namely a multi-photon state.
It will be appreciated that in a quantum system, each photon in a plurality of polarization entangled photon pairs has a respective state, and that the combination of these respective states assumes the state of the quantum system. The quantum state of the quantum system may be a pure state or a mixed state, such as the two-photon NOON state of the two polarization modes prepared in step S101, i.e. a pure state. Pure states represent the quantum states |ψ) of a quantum system) are one defined state. The mixed state represents that the quantum system can have different probabilities P i In different quantum states |ψ i >The mixed state can thus be regarded as a probability distribution of pure states.
Step S302, inputting an optical signal to be detected into a linear optical network, and performing quantum operation on a plurality of polarization entangled photon pairs by utilizing an optical path corresponding to a set of positive operator measurement operators to obtain an output quantum state corresponding to the linear optical network.
In this embodiment, the linear optical network includes a photon in-coupling module 210, a photon manipulation module 220, and a photon output module 230 as shown in fig. 2. The functions of each module are as described in step S102, and will not be described again.
The design of a linear optical network is mainly divided into two parts, one is to determine the number of input ports and output ports of the linear optical network, and the other is to confirm the number of configurations in the linear optical network.
In one implementation, for photon manipulation module 220, the number of positive operator measurement operators may be determined based on the number of polarization modes M comprised by the plurality of polarization entangled photon pairs, and a set of positive operator measurement operators may be designed based on the number of positive operator measurement operators. For example, for the two-photon non state of the two polarization modes prepared in step S101, the photons thereof have two polarization modes, i.e., m=2. Whereas the single photon states of the two polarization modes need to be spread out in the 4-dimensional Hilbert space, so at least 4 positive operator measurement operators are required to reconstruct them. The set of positive operator measurement operators consisting of the 4 positive operator measurement operators described above constitutes the 4 elements of the POVM, measuring the single photon states of the two polarization modes.
Further, since a set of positive operator measurement operators can describe all possible measurements of the quantum state. The POVM of the operator measurement operator by a set of positive operators can obtain measurement results of continuous spectrum physical quantities, and can calculate the probability of occurrence of each measurement result. Thus, on the one hand, the multiphoton states of the two polarization modes can be similarly spread out in the 4-dimensional Hilbert space, and therefore at least 4 positive operator measurement operators are required to reconstruct them. Likewise, a group of positive operator measurement operators consisting of the 4 positive operator measurement operators described above constitutes 4 elements of the POVM, and can also measure multiphoton states of two polarization modes.
Since in the photonic operation module 220 of the linear optical network, the function of the POVM of the set of positive operator measurement operators is implemented using optical paths. Thus, one of the output ports of the linear optical network corresponds one-to-one to one with one of the set of positive operator measurement operators, and the number of output ports of the linear optical network is equal to the number of positive operator measurement operators comprised by the set of positive operator measurement operators.
In one implementation, the number of input ports of the linear optical network may be determined based on the following theoretical analysis process. As shown in the following formula (2),
if the plurality of polarization entangled photon pairs includes a photon number n=1 and the plurality of polarization entangled photon pairs includes a polarization mode number m=2, the input port number R of the linear optical network may be determined according to equation (2) N,M =2. Wherein,representing a combination of values.
In addition, when the plurality of polarization entangled photon pairs comprises lightA sub-number n=1, a number m=2 of polarization modes comprised by the plurality of polarization entangled photon pairs, a number R of input ports of the linear optical network N,M When=2 and the number of output ports M' =4 of the linear optical network, the number of configurations required for the linear optical network can be determined according to the following equation (3):
by calculation of formula (3), R is found N,M,M′ <1. As can be seen from the calculation result, when the number of input ports R of the linear optical network N,M When the number of output ports of the linear optical network M' =4, =2, the linear optical network can measure the quantum state of the 1-photon 2 polarization mode using one configuration.
When the number N of photon numbers is more than or equal to 2 under the condition that the linear optical network still uses the 2 input port and the 4 output port, the calculation of the formula (3) finds thatTherefore, if the number of photons N contained in the quantum state is equal to or greater than 2, the chromatography of the quantum state can be completed with only one set of configuration using a linear optical network of 2 input ports and 4 output ports as well.
Based on the above, the linear optical network can be used for measuring the optical signal to be measured once, and an output quantum state can be obtained. The linear optical network does not need to adjust the structure and configuration in the process of carrying out multi-photon state chromatography, namely, the linear optical network can only use one set of configuration mode in the process of carrying out one-time complete quantum state measurement, so that the time for carrying out data acquisition in the process of quantum state chromatography can be saved.
For the quantum state prepared in step S101, it is necessary to design a 2-input-port-4-output-port linear optical network including a set of 4 positive operator measurement operators { pi } 1 ，π 2 ，π 3 ，π 4 And } to implement the POVM. Wherein 4 positive operator measurementsThe operators are distributed symmetrically in space, all positive operators measure that the operators meet hermite, and the sum of the operators meets the identity operator sigma n Π n ＝1。
In one implementation, corresponding elements may be selected on the surface of a Bloch sphere as positive operator measurement operators, and to ensure their symmetry, four vertices of any inscribed regular tetrahedron in the Bloch sphere may be used as a set of positive operator measurement operators, and the set of positive operator measurement operators thus obtained may be represented by the following formulas (4) - (7):
|π 1 >＝|H>， (4)
wherein pi 1 、π 2 、π 3 And pi 4 A positive operator measurement operator, |H, representing the set of positive operator measurement operators, respectively>And |V>Each representing a polarization mode of the plurality of polarization entangled photons.
And inputting the optical signal to be detected into a designed linear optical network, and performing quantum operation on the plurality of polarization entangled photon pairs by utilizing the optical paths corresponding to the set of positive operator measurement operators determined by the formulas (4) - (7), so that an output quantum state corresponding to the linear optical network can be obtained.
The quantum operation realizes the function of measuring the quantum state based on a group of positive operator measuring operators, the optical path is realized by a polarization beam splitter and a glass slide in a linear optical network, and the output quantum state is expressed as a projection result of the quantum state on the group of positive operator measuring operators.
Fig. 4 shows a schematic structural diagram of an optical path according to an embodiment of the present application.
As shown in fig. 4, BD1 to BD5 are polarizing beam splitters, and the component of the H-polarization mode and the component of the V-polarization mode in the incident light can be spatially separated (the separation distance depends on the thickness of the beam splitter, and typically the separation distance of the two light beams is not less than 4 mm), thereby achieving an operation of converting photons from the polarization mode to the spatial mode. H1 to H5 are half wave plates, Q1 is a quarter slide, and the angles of all slides are shown in table 1 below:
TABLE 1
| H1 | H2 | H3 | H4 | H5 | H6 | Q1 |
| -22.5° | 45° | 67.5° | 17.63° | 45° | 52.5° | 45° |
Wherein the slide functions to add a fixed phase delay between the components of the H-polarization mode and the V-polarization mode and to implement the two-beam optical interference effect into the expressions of the set of positive operator measurement operators listed in equations (4) - (7).
The optical path of the linear optical network shown in fig. 4 uses two polarization input modes, and only the path mode is detected at the output port after the conversion from polarization to path mode, and the detection of the polarization mode is not required. The 1-path port in FIG. 4 corresponds to pi in equation (4) 1 The latter ports are analogized one-to-one. The design of the angle and interference of the slide in the linear optical network is defined as a set of network configurations, i.e. R in equation (3) N，M，M′ . At this time, the linear optical network meets the design requirement of 2 input ports and 4 output ports, and the configuration quantity in the network is 1.
Step S303, the photon number resolvable detector is utilized to obtain the measurement results of the optical paths, probability statistics is carried out on the measurement results of a plurality of optical paths obtained by measuring the optical signals to be measured according to the target times, and a density matrix corresponding to the quantum state of the quantum system is obtained.
In this embodiment, the photon-number-resolvable detector is a detector capable of detecting multiphoton simultaneously.
The two-photon NOON state of the two polarization modes prepared in the step S101 is input into the linear optical network, and the number of times that each photon in the plurality of polarization entangled photon pairs is output from each output port of the linear optical network is counted based on the projection results respectively corresponding to the plurality of output quantum states.
For the optical path of the linear optical network shown in fig. 4, the detection is performed on the output ports 1-4 using photon number-resolving detectors, and the detection results can be divided into two main categories, respectively: 2 photons are simultaneously output from the same port, and two photons are simultaneously output from different ports. Since two photons in the two-photon NOON state of the two polarization modes are indistinguishable, all acquired experimental data can only obtain 10 different combined counting results through measurement of the optical signals to be detected of target times. But from a data processing point of view, 16 sets of counting results are needed to achieve the final solution.
In one implementation, the calculation of the probability may be performed by deriving 16 sets of results based on 10 different combinations of count results. When probability statistics is carried out on the measurement results of a plurality of optical paths obtained by measuring the optical signals to be measured for the target times, data corresponding to the counting results of 10 different combinations can be respectively used as C 11 ，C 22 ，C 33 ，C 44 ，C 12 ，C 13 ，C 14 ，C 23 ，C 24 And C 34 The subscript indicates the port number of the photon output, where C 11 C is the count result of two photons output from port 1 12 Representing the results of 2 photons output from ports 1, 2, respectively, and so on. Since two photons in the two-photon NOON state of the two polarization modes are indistinguishable, count C 12 Whether one photon is output from the port 1 or the port 2 can not be detected, and can be expressed as C by using a mathematical expression 12 ＝C 21 . By analogy, missing data can be compensated in the calculation process when times are summed in such a way that 16 complete sets of data can be deduced from 10 sets of outputs to calculate the probability distribution P corresponding to the port i I represents the port number of the linear optical network.
Probability distribution P obtained from the above data processing i The mathematical expression of the density matrix rho of the quantum state can be solved through a formula (8), so that the operation of quantum state chromatography is completed. Equation (8) is shown below:
P i ＝tr(ρΠ i ) (8)
there are many methods for constructing quantum measurement, in which a linear optical network is used to construct a POVM, a photon number resolvable detector is used to detect the photon number output by the port at the output port of the linear optical network, and finally, a computer is used to process the photon number to obtain a density matrix ρ of the quantum state to be measured.
By way of example, since the linear optical network shown in fig. 4 is constructed using optics, the operating environment of the linear optical network includes a set of temperatures ranging from 25-27 ℃ and one standard atmosphere.
In addition, when the optical signal to be measured is input into the linear optical network, the optical fiber coupling device can be used for receiving the optical signal to be measured, and the optical fiber polarization maintaining device and the polarization operating device can be used for processing the optical signal to be measured.
When the photon number distinguishable detector is used for obtaining the measurement result of the optical path, the optical signal obtained after quantum operation can be processed by using the optical fiber polarization maintaining device and the polarization operation device. And outputting the processed optical signal by using an optical fiber coupler, and receiving the processed optical signal by using a photon number distinguishable detector so as to obtain an output quantum state.
The processing process can improve the pure state of the optical signal to be detected and improve the quality of multiphoton state chromatography.
Therefore, the process of measuring the quantum state based on a set of positive operator measuring operators, which is usually realized by a computer, is converted into an optical path consisting of optical devices to be realized, and the efficiency of quantum state chromatography can be improved.
It should be noted that while in the above embodiments, the operations of the methods of the embodiments are described in a particular order, this does not require or imply that the operations must be performed in that particular order or that all of the illustrated operations be performed in order to achieve desirable results. Rather, the steps depicted in the flowcharts may change the order of execution. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step to perform, and/or one step decomposed into multiple steps to perform.
The foregoing describes specific embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative elements and steps are described above generally in terms of function in order to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, in a software module executed by a processor, or in a combination of the two. The software modules may be disposed in Random Access Memory (RAM), memory, read only memory (R0M), electrically programmable R0M, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The foregoing embodiments have been provided for the purpose of illustrating the general principles of the present application, and are not meant to limit the scope of the invention, but to limit the scope of the invention.
Claims (10)
1. A multi-photon state chromatography method based on a linear optical network, the method comprising:
acquiring an optical signal to be detected; the quantum system corresponding to the optical signal to be detected comprises a plurality of polarization entangled photon pairs, and the quantum state of the quantum system is a pure state or a mixed state;
inputting the optical signal to be detected into the linear optical network, and performing quantum operation on the polarization entangled photon pairs by utilizing an optical path corresponding to a set of positive operator measurement operators to obtain an output quantum state corresponding to the linear optical network; the quantum operation realizes the function of measuring the quantum state based on the set of positive operator measurement operators, the optical path is realized by a polarization beam splitter and a glass slide in the linear optical network, and the output quantum state is expressed as a projection result of the quantum state on the set of positive operator measurement operators;
acquiring measurement results of the optical paths by using a photon number distinguishable detector, and carrying out probability statistics on the measurement results of a plurality of optical paths obtained by measuring the optical signals to be measured for target times to obtain a density matrix corresponding to the quantum state of the quantum system; the density matrix is used to represent the pure state or the mixed state.
2. The method of claim 1, the number of input ports of the linear optical network being determined according to the following formula:
wherein R is N，M Representing the number of input ports of the linear optical network, N representing the number of photons comprised by the plurality of polarization entangled-photon pairs, and M representing the number of polarization modes comprised by the plurality of polarization entangled-photon pairs.
3. The method of claim 1, the number of output ports of the linear optical network being equal to a number of positive operator measurement operators comprised by the set of positive operator measurement operators, one of the output ports being in one-to-one correspondence with one of the set of positive operator measurement operators, the number of positive operator measurement operators being determined from a number of polarization modes comprised by the plurality of polarization entangled photon pairs.
4. The method according to claim 1, wherein the probability statistics of the measurement results of the optical paths obtained by measuring the optical signal to be measured by the target number of times includes:
based on projection results respectively corresponding to a plurality of output quantum states, counting the output times of each photon in the plurality of polarization entangled photon pairs from each output port of the linear optical network to obtain statistical data;
calculating probability distribution corresponding to each output port of the linear optical network based on the statistical data;
and solving a density matrix corresponding to the quantum state of the quantum system based on the probability distribution.
5. The method of claim 1, the set of positive operator measurement operators being represented by the following formula:
|π 1 >＝|H>，
wherein pi 1 、π 2 、π 3 And pi 4 A positive operator measurement operator, |H, representing the set of positive operator measurement operators, respectively>And |V>Each representing a polarization mode of the plurality of polarization entangled photons.
6. The method of claim 1, the acquiring the optical signal under test comprising:
preparing single photons by using a spontaneous parametric down-conversion technique;
and carrying out optical interference and modulation on the plurality of single photons to obtain the plurality of polarization entangled photon pairs so as to obtain the optical signal to be detected.
7. The method of claim 1, the inputting the optical signal under test into the linear optical network, comprising:
receiving the optical signal to be detected by using an optical fiber coupling device;
and processing the optical signal to be detected by using an optical fiber polarization maintaining device and a polarization operation device.
8. The method of claim 1, the obtaining the measurement of the optical path with a photon-number-resolvable detector, comprising:
processing the optical signal obtained after the quantum operation by using an optical fiber polarization maintaining device and a polarization operation device;
outputting the optical signals obtained after the processing by using an optical fiber coupler;
and receiving the optical signal obtained after the processing by using a photon number distinguishable detector so as to obtain a measurement result of the optical path.
9. The method of claim 1, the structure and configuration of the linear optical network during the multi-photon state chromatography remains unchanged.
10. The method of claim 1, wherein the operating environment of the linear optical network comprises a set of temperatures of 25-27 ℃ and one standard atmospheric pressure.
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