Phase measurement method and system based on enhancement of variable beam splitter

Abstract

The invention discloses a phase measurement method and system based on enhancement of a variable beam splitter, and relates to the technical field of quantum precision measurement, and the method comprises the steps: preparing two light sources, and enabling the two light sources to be in a coherent state and a superposed coherent state respectively; taking the coherent state and the superposed coherent state as the input of a first beam splitter of the interferometer, and obtaining a measurement probe from the output port of the beam splitter; a measurement probe obtains a quantum state containing an unknown phase through a phase code related to an unknown parameter, and meanwhile, a photon loss process in a phase coding process is simulated by using a virtual beam splitter; and calculating the quantum Fisher information of the quantum state, and performing numerical optimization on the transmissivity of the first beam splitter in the calculation result to obtain the maximum limit of the quantum Fisher information. Under the condition of certain light intensity, the transmittance of the beam splitter is optimized, so that the phase measurement precision can be improved, the method is easier to implement in experiments, and the practicability is high.

Description

Technical Field

[0001] The present invention relates to the field of quantum precision measurement technology, and in particular to a phase measurement method and system based on variable beam splitter enhancement. Background Art

[0002] Interferometer is one of the most precise measuring instruments with a wide range of applications, such as gravitational wave measurement, quantum sensing, quantum imaging, etc. In theoretical research, the measurement of unknown phase is converted into the relative phase measurement between the two optical paths of the interferometer. Therefore, the accuracy of phase measurement becomes a key factor in determining the performance of precision measurement. According to theoretical research, the accuracy limit of phase measurement is limited by the Heisenberg limit. Joo et al. proposed to use entangled coherent states as probes to perform phase measurement in interferometers. Their research showed that entangled coherent states can exceed the Heisenberg limit under ideal conditions and can still reach the Heisenberg limit even in weak loss scenarios. However, in their method, the transmittance of the interferometer's beam splitter is fixed. The present invention can further improve the phase measurement accuracy limit of entangled coherent states by optimizing and adjusting the transmittance of the first beam splitter of the interferometer, which is of great significance in actual phase measurement. Summary of the invention

[0003] In view of the above-mentioned problems, the present invention is proposed.

[0004] Therefore, the technical problem solved by the present invention is: how to further improve the phase measurement accuracy limit of the entangled coherent state by adjusting the transmittance of the beam splitter.

[0005] To solve the above technical problems, the present invention provides the following technical solutions: a phase measurement method based on variable beam splitter enhancement, comprising: preparing two light sources so that they are in a coherent state and a superposition coherent state respectively; using the coherent state and the superposition coherent state as the input of the first beam splitter of the interferometer, and obtaining a measurement probe from the output port of the beam splitter; the measurement probe is subjected to a phase encoding related to an unknown parameter to obtain a quantum state containing an unknown phase, and a virtual beam splitter is used to simulate the photon loss process in the phase encoding process; the quantum Fisher information of the quantum state is calculated, and the maximum limit of the quantum Fisher information is obtained by numerically optimizing the transmittance of the first beam splitter in the calculation result.

[0006] As a preferred solution of the phase measurement method based on variable beam splitter enhancement described in the present invention, the coherent state is expressed as: The superposition coherent state is expressed as: Where N α Represents the normalization coefficient, the specific form is:

[0007] As a preferred solution of the phase measurement method based on variable beam splitter enhancement described in the present invention, the specific form of the beam splitter is: The obtained measurement probe is represented as: |ECS> τ =N α (|βχ + > a |β(χ - ) b >+|-βχ - > a |βχ + > b 0;

[0008] in and denote the generation and annihilation operators of the a and b optical paths respectively, τ denotes the transmittance of the first beam splitter, When τ=1 / 2, it returns to the symmetric entangled coherent state: |ECS>=N α (|α> a |0> b +|0> a |α> b ).

[0009] As a preferred solution of the phase measurement method based on variable beam splitter enhancement described in the present invention, when the measurement probe first undergoes photon loss and then phase encoding, the photon loss process includes: a virtual beam splitter Used on light path a and the environment state to simulate the photon representation of light path a, They represent the creation and annihilation operators of the ambient state respectively, T represents the transmittance of the virtual beam splitter, T=1 means no photons are lost, and T=0 means all photons are lost.

[0010] As a preferred solution of the phase measurement method based on variable beam splitter enhancement described in the present invention, the measurement probe after loss is represented as:

[0011]

[0012] Then the mixed state is obtained by tracing the ambient mode:

[0013]

[0014] in,

[0015] As a preferred solution of the phase measurement method based on variable beam splitter enhancement described in the present invention, when the quantum state containing unknown parameters is obtained as a bimodal state, the quantum Fisher information solution includes assuming that the orthogonal decomposition form of the density matrix of the probe is:

[0016]

[0017] After phase encoding, the density matrix is ​​expressed as:

[0018]

[0019] The quantum Fisher information calculation formula is:

[0020]

[0021] Among them, p i is the eigenvalue of the initial state, |ψ i > is the eigenstate,

[0022] As a preferred solution of the phase measurement method based on variable beam splitter enhancement described in the present invention, wherein: the quantum Fisher information calculation formula is simplified to obtain: φ =4p1(ΔH1) 2 +4p2(ΔH2) 2 -16p1p2|(ΔH 12 )| 2 , by numerically optimizing the transmittance τ of the first beam splitter in the calculation results, the maximum limit of quantum Fisher information can be obtained.

[0023] Another object of the present invention is to provide a phase measurement system based on variable beam splitter enhancement, comprising: a beam splitter, a virtual beam splitter and a detector; the beam splitter is used to input coherent states and superposition coherent states to obtain a measurement probe; the virtual beam splitter is used to simulate the photon loss process in the phase encoding process; the detector collects the results after beam splitter enhancement through the sensors thereon.

[0024] Beneficial effects of the present invention: The phase measurement method and system based on variable beam splitter enhancement provided by the present invention can further improve the phase measurement accuracy limit by optimizing the transmittance of the first beam splitter, and can also maintain the robustness of the phase measurement accuracy in the presence of photon loss. This method only requires the optimization of the passive linear optical device, the beam splitter, which is easier to implement experimentally and has strong practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0026] Figure 1 An overall flow chart of a phase measurement method based on variable beam splitter enhancement provided by one embodiment of the present invention;

[0027] Figure 2 A schematic diagram of the phase measurement principle of a phase measurement method based on variable beam splitter enhancement provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0028] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0029] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0030] Example 1

[0031] Reference Figure 1-Figure 2 , as an embodiment of the present invention, provides a phase measurement method based on variable beam splitter enhancement, comprising:

[0032] S1: prepare two light sources so that they are in a coherent state and a superposition coherent state respectively;

[0033] Furthermore, the coherent state is expressed as: The superposition coherent state is expressed as: Where N α Represents the normalization coefficient, the specific form is:

[0034] S2: The coherent state and the superposition coherent state are used as the input of the first beam splitter of the interferometer, and the measurement probe is obtained from the output port of the beam splitter;

[0035] Furthermore, the specific form of the beam splitter is: The resulting measurement probe is represented by: |ECS> τ =N α (|βχ + > a |β(χ - ) b >+|-βχ- > a |βχ + > b );

[0036] in and denote the generation and annihilation operators of the a and b optical paths respectively, τ denotes the transmittance of the first beam splitter, Subscripts a and b represent two optical paths respectively. When τ = 1 / 2, it returns to the symmetric entangled coherent state: |ECS> = N α (|α> a |0> b +|0> a |α> b ), unlike the traditional interferometer, the transmittance of the first beam splitter of the present invention is variable and not fixed.

[0037] S3: The measurement probe undergoes a phase encoding related to an unknown parameter to obtain a quantum state containing an unknown phase, and a virtual beam splitter is used to simulate the photon loss process during the phase encoding process;

[0038] Furthermore, since the unitary operators representing phase encoding and photon loss satisfy the commutation relation,

[0039] For the convenience of calculation, the probe first undergoes photon loss and then phase encoding. A virtual beam splitter is used for photon loss: Used on light path a and the environment state to simulate the photon representation of light path a, They represent the generation and annihilation operators of the ambient state, T represents the transmittance of the virtual beam splitter, T = 1 means no photon is lost, T = 0 means all photons are lost, and the ambient state is assumed to be a vacuum state. After the loss, the specific form of the probe is:

[0040] Then the mixed state is obtained by tracing the ambient mode:

[0041]

[0042] in,

[0043] S4: Calculate the quantum Fisher information of the quantum state and obtain the maximum limit of the quantum Fisher information by numerically optimizing the transmittance of the first beam splitter in the calculation results.

[0044] It should be noted that As a probe measuring the unknown phase after photon loss, the unitary operator of a general single phase can generally be expressed as: Here φ represents the phase probe related to the unknown parameters, which can be expressed as follows after the phase encoding process: The quantum state containing unknown parameters is obtained, and the limit of its measurement accuracy is calculated using quantum Fisher information theory. Taking the general dual-mode state as an example, the process of solving quantum Fisher information is as follows:

[0045] Assume that the orthogonal decomposition form of the probe density matrix is:

[0046] After phase encoding, the density matrix is ​​expressed as:

[0047]

[0048] The quantum Fisher information calculation formula is:

[0049]

[0050] Among them, p i is the eigenvalue of the initial state, |ψ i > is the eigenstate,

[0051] Furthermore, the above formula can be simplified to obtain: φ =4p1(ΔH1) 2 +4p2(ΔH2) 2 -16p1p2|(ΔH 12 )| 2 In this case, |ψ>1=|βχ + >1|βχ - >2,|ψ>2=|-βχ - >1|βχ + >2.

[0052] The analytical solution of quantum Fisher information can be obtained through the above-mentioned solution formula of quantum Fisher information. By numerically optimizing the transmittance of the first beam splitter in the calculation results, the maximum limit of quantum Fisher information can be obtained.

[0053] Example 2

[0054] As an embodiment of the present invention, a digital construction system for typical planning scenarios of county distribution networks is provided, including:

[0055] Beam splitters, virtual beam splitters, and detectors;

[0056] The beam splitter is used to input the coherent state and the superposition coherent state to obtain the measurement probe;

[0057] The virtual beam splitter is used to simulate the photon loss process during phase encoding;

[0058] The detector collects the results of the beam splitter enhancement through the sensors on it.

[0059] Example 3

[0060] As an embodiment of the present invention, a phase measurement method based on variable beam splitter enhancement is provided. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0061] In the case of α = 4 (the average number of photons is equal to 16), we plan to verify the performance advantage of this scheme. Compared with the original scheme, this scheme allows the beam splitter transmittance in the interferometer to be variable. In the actual measurement process, photon loss is inevitable, which will seriously affect the measurement accuracy. However, by optimizing the beam splitter transmittance, this scheme can significantly improve the measurement accuracy in the presence of photon loss, showing obvious advantages over the original scheme. The simulation results are shown below:

[0062] Table 1 Comparison of quantum Fisher information when photon loss occurs

[0063] Photon loss rate This program Original plan Gain 5％ <![CDATA[F opt =150.93]]> <![CDATA[F B =134.21]]> G＝12.4％ 10％ <![CDATA[F opt =99.20]]> <![CDATA[F B =70.66]]> G＝40.4％ 15％ <![CDATA[F opt =73.37]]> <![CDATA[F B =43.98]]> G＝66.8％ 20％ <![CDATA[F opt =57.86]]> <![CDATA[F B =32.27]]> G＝79.3％ 25％ <![CDATA[F opt =47.37]]> <![CDATA[F B =26.64]]> G＝77.8％ 30％ <![CDATA[F opt =39.73]]> <![CDATA[F B =23.43]]> G＝69.5％ 35％ <![CDATA[F opt =33.80]]> <![CDATA[F B =21.20]]> G＝59.4％ 40％ <![CDATA[F opt =29.00]]> <![CDATA[F B =19.35]]> G＝49.9％

[0064] Among them, F opt The maximum value of the quantum Fisher information that can be obtained by this scheme (the larger the value, the higher the accuracy), compared with the scheme using a balanced beam splitter (F B ), this scheme can achieve a higher accuracy limit.

[0065] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A phase measurement method based on variable beam splitter enhancement, characterized in that: include: Two light sources are prepared so that they are in a coherent state and a superposition coherent state respectively; Using the coherent state and the superposition coherent state as the input of the first beam splitter of the interferometer, and obtaining a measurement probe from the output port of the beam splitter; The measuring probe is subjected to a phase encoding related to an unknown parameter to obtain a quantum state containing an unknown phase, and a virtual beam splitter is used to simulate the photon loss process during the phase encoding process; The quantum Fisher information of the quantum state is calculated, and the maximum limit of the quantum Fisher information is obtained by numerically optimizing the transmittance of the first beam splitter in the calculation result.

2. The phase measurement method based on variable beam splitter enhancement as claimed in claim 1, characterized in that: The coherent state is expressed as: The superposition coherent state is expressed as: Where N α Represents the normalization coefficient, the specific form is:

3. The phase measurement method based on variable beam splitter enhancement as claimed in claim 2, characterized in that: The specific form of the beam splitter is: The obtained measurement probe is represented as: |ECS> τ =N α (|βχ + > a |β(χ - ) b >+|-βχ-> a |βχ + > b ); in and denote the generation and annihilation operators of the a and b optical paths respectively, τ denotes the transmittance of the first beam splitter, When τ=1 / 2, it returns to the symmetric entangled coherent state: |ECS>=N α (|α> a |0> b +|0> a |α> b ).

4. The phase measurement method based on variable beam splitter enhancement as claimed in claim 3, characterized in that: When the measurement probe undergoes photon loss and then phase encoding, the photon loss process includes a virtual beam splitter. Used on light path a and the environment state to simulate the photon representation of light path a, They represent the creation and annihilation operators of the ambient state respectively, T represents the transmittance of the virtual beam splitter, T=1 means no photons are lost, and T=0 means all photons are lost.

5. The phase measurement method based on variable beam splitter enhancement as claimed in claim 4, characterized in that: The measurement probe after loss is represented as: Then the mixed state is obtained by tracing the ambient mode: in, 6. The phase measurement method based on variable beam splitter enhancement as claimed in claim 5, characterized in that: When the quantum state containing unknown parameters is obtained as a bimodal state, the quantum Fisher information solution includes assuming that the orthogonal decomposition form of the density matrix of the probe is: After phase encoding, the density matrix is ​​expressed as: The quantum Fisher information calculation formula is: Among them, p i is the eigenvalue of the initial state, |ψ i > is the eigenstate, 7. The phase measurement method based on variable beam splitter enhancement as claimed in claim 6, characterized in that: The quantum Fisher information calculation formula is simplified to: φ =4p1(ΔH1) 2 +4p2(ΔH2) 2 -16p1p 2| |(|(ΔH 12 )| 2 , by numerically optimizing the transmittance τ of the first beam splitter in the calculation results, the maximum limit of quantum Fisher information can be obtained.

8. A system using the phase measurement method based on variable beam splitter enhancement as claimed in any one of claims 1 to 7, characterized in that: include: Beam splitters, virtual beam splitters, and detectors; The beam splitter is used to input a coherent state and a superposition coherent state to obtain a measurement probe; The virtual beam splitter is used to simulate the photon loss process in the phase encoding process; The detector collects the results of the beam splitter enhancement through the sensing thereon.

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