Noise suppression method and system based on weak measurement sensing system

Abstract

The application provides a noise suppression method and system based on a weak measurement sensing system, comprising: building a quantum weak measurement optical platform, not introducing a to-be-measured parameter in a weak coupling process, preliminarily measuring the system, and obtaining a power spectrum of coupling noise according to system output; introducing the to-be-measured parameter in the weak coupling process, measuring the system, and obtaining system output mixed by the to-be-measured parameter and the coupling noise; calculating a power spectrum of the system output and reserving phase information, deducting a noise power spectrum from the power spectrum of the system output, combining the reserved phase information, obtaining a restored real signal spectrum, and restoring the real signal by inverse Fourier transform; judging whether there is residual noise in the restored real signal, and eliminating the residual non-stationary noise by using singular spectrum analysis. The application utilizes weak value amplification technology, can achieve very high measurement accuracy, i.e. approaching the limit of shot noise, and suppresses part of technical noise such as relative intensity noise from a hardware level.

Description

Technical Field

[0001] This invention relates to the field of weak measurement technology, and more specifically, to a noise suppression method and system based on a weak measurement sensing system. Background Technology

[0002] Since its inception, weak measurement technology has been widely applied in various sensing systems due to its advantages, including the ability to amplify extremely small physical quantities using weak values, high theoretical accuracy (approaching the shot noise limit), and the ability to suppress some technical noise. However, in the practical implementation of weak measurement-based sensing systems, such as fiber-optic weak measurement gyroscopes, a significant amount of technical noise is generated, originating from sources including light sources, electrical components, and physical fields. While this technical noise contains valuable information about the physical system, it severely affects the accuracy and stability of the weak measurement sensing system. Therefore, how to design corresponding algorithms to suppress noise during actual physical parameter measurements using the acquired noise information has been a persistent problem for researchers.

[0003] Patent document CN115574940A discloses a method and system for suppressing polarization-induced phase noise in a weak measurement system, comprising the following steps: Step 1: Constructing a fiber-optic-based quantum weak measurement optical system with time-division polarization switching function, emitting light pulses at a preset frequency from a light source, and modulating the polarization state of each incident light pulse at the same frequency using a polarization switcher; Step 2: Introducing a reference phase to make the system operate within a preset sensitivity and dynamic range; Step 3: Synchronizing and controlling the optical path switcher with an external clock; Step 4: Receiving light pulses through a balanced detector and calculating the signal-to-noise ratio (SNR) of the current output signal; Step 5: If the current SNR is higher than the preset SNR, noise suppression is achieved; otherwise, the polarization switching rate is increased, and steps 2-5 are repeated. However, this invention does not effectively suppress stationary and non-stationary noise in the output data of the weak measurement system. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a noise suppression method and system based on a weak measurement sensing system.

[0005] A noise suppression method based on a weak measurement sensing system provided by the present invention includes:

[0006] Step S1: Construct a quantum weak measurement optical platform. Without introducing the parameter to be measured during the weak coupling process, perform preliminary measurements on the system and obtain the power spectrum of the coupling noise based on the system output.

[0007] Step S2: Introduce the parameter to be measured during the weak coupling process, measure the system, and obtain the system output that is a mixture of the parameter to be measured and the coupling noise;

[0008] Step S3: Calculate the power spectrum of the system output and retain the phase information. Subtract the noise power spectrum from the system output power spectrum. Combine the retained phase information to obtain the recovered true signal spectrum. Perform an inverse Fourier transform on the recovered spectrum to recover the true signal.

[0009] Step S4: For the recovered real signal, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise.

[0010] Preferably, in step S1:

[0011] Step S1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during the weak coupling process, generating a time-varying phase parameter n(t). After interaction, the state of the output light is...

[0012] Where i represents the input state of the system, i.e., the polarization state of the photon. This represents the interaction between the system and the pointer. p represents the pointer, i.e., the angular frequency of the photon, t is time, and n(t) is the random coupling noise introduced during the interaction process;

[0013] Step S1.2: The post-selected state is modulated to |f(t)>, and the weakly coupled light is projected onto the post-selected state. The state of the output light after projection is represented as |φ. f (t)>= <f|Φ i >; Based on the required detection frequency f, the two post-selective states are modulated as follows: as well as

[0014] Step S1.3: Use the center frequency of the photon as the detection index. The detection was performed using a spectrometer. The spectrometer detection time was T, and the spectrometer output was...

[0015] in, Here, ω is the momentum operator, i.e., the angular frequency of the photon; t0 is the start time of the measurement; and N is the energy of the output light collected during the time interval [t0, t0+T].

[0016] Step S1.4: The two spectrometer outputs corresponding to the post-selected states |f1(t)> and |f2(t)> <p f > T Calculate respectively as well as This corresponds to the real and imaginary parts of the spectrum of the noise at frequency f at this time;

[0017] Where, nT (t) represents the noise n(t) during the time interval [t0, t0+T], and is 0 for the rest of the time interval. N is the energy of the output light collected during the time interval [t0, t0+T]. <p f > T Let N0 be the center frequency of the output light collected within the time interval [t0, t0+T], and let N0 be the luminous efficiency of the light source. i The center frequency of the light source;

[0018] Calculate the spectrum of the noise at frequency f. The power spectrum of the noise can be calculated using Wiener-Khinchin's theorem:

[0019] Preferably, in step S2:

[0020] By employing weak amplification schemes, including standard weak amplification or bias weak amplification, the time-varying parameter g(t) to be measured is introduced during the interaction process to obtain the noisy system output y(kT). d ), k = 1, 2, ..., T d This refers to the data sampling period.

[0021] Preferably, in step S3:

[0022] System output y(kT) d The relationship between y(kT) and the real signal g(t) and noise n(t) is given by y(kT) d )=g(kT d )+n(kT d The real signal and noise are uncorrelated, and the noise is a zero-mean stationary process, |G(ω)| 2 =E[|Y(ω)| 2 ]-S N (ω); where G(ω) is the spectrum of the real signal, Y(ω) is the spectrum of the noisy signal, and S N (ω) represents the power spectrum of the noise, and E represents the statistical mean; if the autocorrelation function of the noise satisfies ergodicity, then we obtain...

[0023] Φ X (ω)≈Φ Y (ω), Perform inverse Fourier transform to recover g(kT) d );

[0024] Where, Φ X (ω) is the phase spectrum of the real signal, Φ Y (ω) represents the phase spectrum of the noisy signal.

[0025] Preferably, in step S4:

[0026] Step S4.1: Select the embedding dimension L, and embed the denoised time series y(kT) into the desired embedding dimension L. d Embedded into its L-dimensional phase space, generating a noisy manifold Y in the phase space:

[0027]

[0028] Among them, Y K L represents the number of phase points embedded into the phase space with L as the embedding dimension, and K = N - L + 1 represents the number of phase points embedded into the phase space.

[0029] Step S4.2: Select sub-dimension R, and select R mutually orthogonal directions (u1, u2, ..., u3) in the phase space. R This maximizes the energy variance of the noisy manifold in these R directions:

[0030]

[0031] Where r is the subscript of the feature direction to be sought, Y k For phase points embedded into phase space;

[0032] Step S4.3: Project the noisy manifold Y onto the R directions obtained in step S4.2 to obtain the manifold G of the true signal, and recover the true signal g(kT) by anti-diagonal averaging of the true signal manifold G. d ).

[0033] A noise suppression system based on a weak measurement sensing system provided by the present invention includes:

[0034] Module M1: Constructs a quantum weak measurement optical platform, which does not introduce the parameter to be measured during the weak coupling process, performs preliminary measurements on the system, and obtains the power spectrum of the coupling noise based on the system output;

[0035] Module M2: Introduces the parameter to be measured during the weak coupling process, measures the system, and obtains the system output that is a mixture of the parameter to be measured and the coupling noise;

[0036] Module M3: Calculates the power spectrum of the system output and retains the phase information. Subtracts the noise power spectrum from the system output power spectrum and combines it with the retained phase information to obtain the recovered true signal spectrum. Performs an inverse Fourier transform on the recovered spectrum to recover the true signal.

[0037] Module M4: For the recovered real signal, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise.

[0038] Preferably, in module M1:

[0039] Module M1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during the weak coupling process, generating a time-varying phase parameter n(t). After interaction, the state of the output light is...

[0040] Where i represents the input state of the system, i.e., the polarization state of the photon. This represents the interaction between the system and the pointer. p represents the pointer, i.e., the angular frequency of the photon, t is time, and n(t) is the random coupling noise introduced during the interaction process;

[0041] Module M1.2: The post-selection state is modulated as |f(t)>, and the weakly coupled light is projected onto the post-selection state. The state of the output light after projection is represented as |φ. f (t)>= <f|Φ i >; Based on the required detection frequency f, the two post-selective states are modulated as follows: as well as

[0042] Module M1.3: Uses the center frequency of photons as the detection index. The detection was performed using a spectrometer. The spectrometer detection time was T, and the spectrometer output was...

[0043] in, Here, ω is the momentum operator, i.e., the angular frequency of the photon; t0 is the start time of the measurement; and N is the energy of the output light collected during the time interval [t0, t0+T].

[0044] Module M1.4: Two spectrometer outputs corresponding to the post-selection states |f1(t)> and |f1(t)>. <p f > T Calculate respectively as well as This corresponds to the real and imaginary parts of the spectrum of the noise at frequency f at this time;

[0045] Where, n T (t) represents the noise n(t) during the time interval [t0, t0+T], and is 0 for the rest of the time interval. N is the energy of the output light collected during the time interval [t0, t0+T]. <p f > T Let N0 be the center frequency of the output light collected within the time interval [t0, t0+T], and let N0 be the luminous efficiency of the light source. i The center frequency of the light source;

[0046] Calculate the spectrum of the noise at frequency f. The power spectrum of the noise can be calculated using Wiener-Khinchin's theorem:

[0047] Preferably, in module M2:

[0048] By employing weak amplification schemes, including standard weak amplification or bias weak amplification, the time-varying parameter g(t) to be measured is introduced during the interaction process to obtain the noisy system output y(kT). d ), k = 1, 2, ..., T d This refers to the data sampling period.

[0049] Preferably, in module M3:

[0050] System output y(kT) d The relationship between y(kT) and the real signal g(t) and noise n(t) is given by y(kT) d )=g(kT d )+n(kT d The real signal and noise are uncorrelated, and the noise is a zero-mean stationary process, |G(ω)| 2 =E[|Y(ω)| 2 ]-S N (ω); where G(ω) is the spectrum of the real signal, Y(ω) is the spectrum of the noisy signal, and S N (ω) represents the power spectrum of the noise, and E represents the statistical mean; if the autocorrelation function of the noise satisfies ergodicity, then we obtain...

[0051] Φ X (ω)≈Φ Y (ω), Perform inverse Fourier transform to recover g(kT) d );

[0052] Where, Φ X (ω) is the phase spectrum of the real signal, Φ Y (ω) represents the phase spectrum of the noisy signal.

[0053] Preferably, in module M4:

[0054] Module M4.1: Select the embedding dimension L, and denoise the time series y(kT) d Embedded into its L-dimensional phase space, generating a noisy manifold Y in the phase space:

[0055]

[0056] Among them, Y K L represents the number of phase points embedded into the phase space with L as the embedding dimension, and K = N - L + 1 represents the number of phase points embedded into the phase space.

[0057] Module M4.2: Select sub-dimension R, and select R mutually orthogonal directions (u1, u2, ..., u3) in the phase space. R This maximizes the energy variance of the noisy manifold in these R directions:

[0058]

[0059] Where r is the subscript of the feature direction to be sought, Y k For phase points embedded into phase space;

[0060] Module M4.3: Projects the noisy manifold Y onto the R directions obtained from module M4.2 to obtain the manifold G of the true signal, and recovers the true signal g(kT) by anti-diagonal averaging of the true signal manifold G. d ).

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. This invention utilizes weak value amplification technology, which can achieve very high measurement accuracy, i.e., approaching the shot noise limit, from a theoretical model perspective, and suppress some technical noise, such as relative intensity noise, from a hardware level.

[0063] 2. This invention effectively suppresses stationary and non-stationary noise in the output data of weak measurement systems, greatly improving the measurement accuracy and stability of weak measurement systems from an algorithmic perspective. Attached Figure Description

[0064] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0065] Figure 1 A flowchart of a noise suppression scheme for a weak measurement sensing system;

[0066] Figure 2 A comparison chart showing the signal-to-noise ratio improvement with and without spectral subtraction in the presence of stationary noise.

[0067] Figure 3 This is a comparison chart showing the signal-to-noise ratio improvement with and without singular spectrum analysis in the presence of non-stationary noise. Detailed Implementation

[0068] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0069] Example 1:

[0070] This invention provides a noise suppression method for weak measurement sensing systems. The method involves measuring the system without introducing a signal and calculating the noise power spectrum based on the acquired noise information. Under the actual measurement parameters, stationary noise in the output data is filtered out using spectral subtraction. If noise still exists in the output data, the remaining noise can be determined to be non-stationary, and singular spectrum analysis is used to further filter out the remaining noise. The noise suppression method provided in this study, based on weak value amplification, further suppresses noise that is difficult to eliminate through hardware adjustments by using spectral subtraction and singular spectrum analysis, thereby significantly improving the accuracy and stability of weak measurement sensing systems.

[0071] According to the present invention, a noise suppression method based on a weak measurement sensing system is provided, such as... Figures 1-3 As shown, it includes:

[0072] Step S1: Construct a quantum weak measurement optical platform. Without introducing the parameter to be measured during the weak coupling process, perform preliminary measurements on the system and obtain the power spectrum of the coupling noise based on the system output.

[0073] Specifically, in step S1:

[0074] Step S1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during the weak coupling process, generating a time-varying phase parameter n(t). After interaction, the state of the output light is...

[0075] Where i represents the input state of the system, i.e., the polarization state of the photon. This represents the interaction between the system and the pointer. p represents the pointer, i.e., the angular frequency of the photon, t is time, and n(t) is the random coupling noise introduced during the interaction process;

[0076] Step S1.2: The post-selected state is modulated to |f(t)>, and the weakly coupled light is projected onto the post-selected state. The state of the output light after projection is represented as |φ. f (t)>= <f|Φ i >; Based on the required detection frequency f, the two post-selective states are modulated as follows: as well as

[0077] Step S1.3: Use the center frequency of the photon as the detection index. The detection was performed using a spectrometer. The spectrometer detection time was T, and the spectrometer output was...

[0078] in, Here, ω is the momentum operator, i.e., the angular frequency of the photon; t0 is the start time of the measurement; and N is the energy of the output light collected during the time interval [t0, t0+T].

[0079] Step S1.4: The two spectrometer outputs corresponding to the post-selected states |f1(t)> and |f2(t)> are <p f > T Calculate respectively as well as This corresponds to the real and imaginary parts of the spectrum of the noise at frequency f at this time;

[0080] Where, n T (t) represents the noise n(t) during the time interval [t0, t0+T], and is 0 for the rest of the time interval. N is the energy of the output light collected during the time interval [t0, t0+T]. <p f > T Let N0 be the center frequency of the output light collected within the time interval [t0, t0+T], and let N0 be the luminous efficiency of the light source. i The center frequency of the light source;

[0081] Calculate the spectrum of the noise at frequency f. The power spectrum of the noise can be calculated using Wiener-Khinchin's theorem:

[0082] Step S2: Introduce the parameter to be measured during the weak coupling process, measure the system, and obtain the system output that is a mixture of the parameter to be measured and the coupling noise;

[0083] Specifically, in step S2:

[0084] By employing weak amplification schemes, including standard weak amplification or bias weak amplification, the time-varying parameter g(t) to be measured is introduced during the interaction process to obtain the noisy system output y(kT). d ), k = 1, 2, ..., T d This refers to the data sampling period.

[0085] Step S3: Calculate the power spectrum of the system output and retain the phase information. Subtract the noise power spectrum from the system output power spectrum. Combine the retained phase information to obtain the recovered true signal spectrum. Perform an inverse Fourier transform on the recovered spectrum to recover the true signal.

[0086] Specifically, in step S3:

[0087] System output y(kT) d The relationship between y(kT) and the real signal g(t) and noise n(t) is given by y(kT) d )=g(kTd )+n(kT d The real signal and noise are uncorrelated, and the noise is a zero-mean stationary process, |G(ω)| 2 =E[|Y(ω)| 2 ]-S N (ω); where G(ω) is the spectrum of the real signal, Y(ω) is the spectrum of the noisy signal, and S N (ω) represents the power spectrum of the noise, and E represents the statistical mean; if the autocorrelation function of the noise satisfies ergodicity, then we obtain...

[0088] Φ X (ω)≈Φ Y (ω), Perform inverse Fourier transform to recover g(kT) d );

[0089] Where, Φ X (ω) is the phase spectrum of the real signal, Φ Y (ω) represents the phase spectrum of the noisy signal.

[0090] Step S4: For the recovered real signal, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise.

[0091] Specifically, in step S4:

[0092] Step S4.1: Select the embedding dimension L, and embed the denoised time series y(kT) into the desired embedding dimension L. d Embedded into its L-dimensional phase space, generating a noisy manifold Y in the phase space:

[0093]

[0094] Among them, Y K L represents the number of phase points embedded into the phase space with L as the embedding dimension, and K = N - L + 1 represents the number of phase points embedded into the phase space.

[0095] Step S4.2: Select sub-dimension R, and select R mutually orthogonal directions (u1, u2, ..., u3) in the phase space. R This maximizes the energy variance of the noisy manifold in these R directions:

[0096]

[0097] Where r is the subscript of the feature direction to be sought, Y k For phase points embedded into phase space;

[0098] Step S4.3: Project the noisy manifold Y onto the R directions obtained in step S4.2 to obtain the manifold G of the true signal, and recover the true signal g(kT) by anti-diagonal averaging of the true signal manifold G. d ).

[0099] Example 2:

[0100] Example 2 is a preferred embodiment of Example 1, and is used to illustrate the present invention in more detail.

[0101] The present invention also provides a noise suppression system based on a weak measurement sensing system. The noise suppression system based on a weak measurement sensing system can be implemented by executing the process steps of the noise suppression method based on a weak measurement sensing system. That is, those skilled in the art can understand the noise suppression method based on a weak measurement sensing system as a preferred embodiment of the noise suppression system based on a weak measurement sensing system.

[0102] A noise suppression system based on a weak measurement sensing system provided by the present invention includes:

[0103] Module M1: Constructs a quantum weak measurement optical platform, which does not introduce the parameter to be measured during the weak coupling process, performs preliminary measurements on the system, and obtains the power spectrum of the coupling noise based on the system output;

[0104] Specifically, in module M1:

[0105] Module M1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during the weak coupling process, generating a time-varying phase parameter n(t). After interaction, the state of the output light is...

[0106] Where i represents the input state of the system, i.e., the polarization state of the photon. This represents the interaction between the system and the pointer. p represents the pointer, i.e., the angular frequency of the photon, t is time, and n(t) is the random coupling noise introduced during the interaction process;

[0107] Module M1.2: The post-selection state is modulated as |f(t)>, and the weakly coupled light is projected onto the post-selection state. The state of the output light after projection is represented as |φ. f (t)>= <f|Φ i >; Based on the required detection frequency f, the two post-selective states are modulated as follows: as well as

[0108] Module M1.3: Uses the center frequency of photons as the detection index. The detection was performed using a spectrometer. The spectrometer detection time was T, and the spectrometer output was...

[0109] in, Here, ω is the momentum operator, i.e., the angular frequency of the photon; t0 is the start time of the measurement; and N is the energy of the output light collected during the time interval [t0, t0+T].

[0110] Module M1.4: Two spectrometer outputs corresponding to the post-selection states |f1(t)> and |f2(t)>. <p f > T Calculate respectively as well as This corresponds to the real and imaginary parts of the spectrum of the noise at frequency f at this time;

[0111] Where, n T (t) represents the noise n(t) during the time interval [t0, t0+T], and is 0 for the rest of the time interval. N is the energy of the output light collected during the time interval [t0, t0+T]. <p f > T Let N0 be the center frequency of the output light collected within the time interval [t0, t0+T], and let N0 be the luminous efficiency of the light source. i The center frequency of the light source;

[0112] Calculate the spectrum of the noise at frequency f. The power spectrum of the noise can be calculated using Wiener-Khinchin's theorem:

[0113] Module M2: Introduces the parameter to be measured during the weak coupling process, measures the system, and obtains the system output that is a mixture of the parameter to be measured and the coupling noise;

[0114] Specifically, in module M2:

[0115] By employing weak amplification schemes, including standard weak amplification or bias weak amplification, the time-varying parameter g(t) to be measured is introduced during the interaction process to obtain the noisy system output y(kT). d ), k = 1, 2, ..., T d This refers to the data sampling period.

[0116] Module M3: Calculates the power spectrum of the system output and retains the phase information. Subtracts the noise power spectrum from the system output power spectrum and combines it with the retained phase information to obtain the recovered true signal spectrum. Performs an inverse Fourier transform on the recovered spectrum to recover the true signal.

[0117] Specifically, in module M3:

[0118] System output y(kT) dThe relationship between y(kT) and the real signal g(t) and noise n(t) is given by y(kT) d )=g(kT d )+n(kT d The real signal and noise are uncorrelated, and the noise is a zero-mean stationary process, |G(ω)| 2 =E[|Y(ω)| 2 ]-S N (ω); where G(ω) is the spectrum of the real signal, Y(ω) is the spectrum of the noisy signal, and S N (ω) represents the power spectrum of the noise, and E represents the statistical mean; if the autocorrelation function of the noise satisfies ergodicity, then we obtain...

[0119] Φ X (ω)≈Φ Y (ω), Perform inverse Fourier transform to recover g(kT) d );

[0120] Where, Φ X (ω) is the phase spectrum of the real signal, Φ Y (ω) represents the phase spectrum of the noisy signal.

[0121] Module M4: For the recovered real signal, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise.

[0122] Specifically, in module M4:

[0123] Module M4.1: Select the embedding dimension L, and denoise the time series y(kT) d Embedded into its L-dimensional phase space, generating a noisy manifold Y in the phase space:

[0124]

[0125] Among them, Y K L represents the number of phase points embedded into the phase space with L as the embedding dimension, and K = N - L + 1 represents the number of phase points embedded into the phase space.

[0126] Module M4.2: Select sub-dimension R, and select R mutually orthogonal directions (u1, u2, ..., u3) in the phase space. R This maximizes the energy variance of the noisy manifold in these R directions:

[0127]

[0128] Where r is the subscript of the feature direction to be sought, Y k For phase points embedded into phase space;

[0129] Module M4.3: Projects the noisy manifold Y onto the R directions obtained from module M4.2 to obtain the manifold G of the true signal, and recovers the true signal g(kT) by anti-diagonal averaging of the true signal manifold G. d ).

[0130] Example 3:

[0131] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0132] like Figure 1 As shown, the present invention provides a noise suppression scheme for weak measurement sensing systems, comprising:

[0133] Step A: Construct a quantum weak measurement optical platform. Without introducing the parameter to be measured during the weak coupling process, perform preliminary measurements on the system and obtain the power spectrum S of the coupling noise based on the system output. N (f).

[0134] Step B: Introduce the parameter to be measured during the weak coupling process, measure the system, and obtain the system output y(kT) which is a mixture of the parameter to be measured g(t) and the coupling noise n(t). d ), k = 1, 2, ...

[0135] Step C: Output y(kT) from the system d Calculate its power spectrum S Y (f) and retain phase information from S Y (f) Noise power spectrum subtracted from s N (f) Combining the retained phase information, the spectrum of the recovered true signal can be obtained. The true signal can be recovered by performing an inverse Fourier transform on the recovered spectrum.

[0136] Step D: For the real signal recovered from step 3, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise.

[0137] Step A includes the following steps:

[0138] Step A1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during the weak coupling process, generating a time-varying phase parameter n(t). After interaction, the state of the output light is...

[0139] Step A2: The post-selected state is modulated to |f(t)>, and the weakly coupled light is projected onto the post-selected state. The state of the output light after projection is represented by |φ. f (t)>= <f|Φ i>. Based on the required detection frequency f, the two post-selective modulations are as follows: as well as

[0140] Step A3: Use the center frequency of the photon as the detection index If a spectrometer is used for detection, and the detection time of the spectrometer is T, then the output of the spectrometer is: It can collect data for as long as possible to achieve high-precision estimation of noise power spectrum.

[0141] Step A4: The two spectrometer outputs corresponding to the post-selected states |f1(t)> and |f2(t)> <p f > T We can calculate them separately. as well as Since we know the real and imaginary parts of the spectrum of the noise at frequency f, we can further calculate the spectrum of the noise at frequency f. The power spectrum of noise can be calculated using Wiener-Khinchin's theorem:

[0142] Step B includes the following steps: using a general weak amplification scheme, such as standard weak amplification or bias weak amplification, the time-varying parameter g(t) to be measured is introduced during the interaction process to obtain the noisy system output y(kT). d ), k = 1, 2, ...

[0143] Step C includes the following steps: Assume the system outputs y(kT) d The relationship between y(kT) and the real signal g(t) and noise n(t) is given by y(kT) d )=g(kT d )+n(kT d Since the real signal and noise are uncorrelated, and the noise is a zero-mean stationary process, we have |G(ω)| 2 =E[|Y(ω)| 2 ]-S N (ω). If the autocorrelation function of the noise satisfies ergodicity, then we can obtain And assume Φ X (ω)≈Φ Y (ω), therefore Performing an inverse Fourier transform will recover g(kT) d ).

[0144] Step D includes the following steps:

[0145] Step D1: Select the embedding dimension L, and then convert the time series y(kT) after denoising in step C into a single data set.d Embedded into its L-dimensional phase space, generating a noisy manifold Y in the phase space.

[0146]

[0147] Step D2: Select sub-dimension R, and select R mutually orthogonal directions (u1, u2, ..., u3) in the phase space. R This maximizes the energy, i.e., the variance, of the noisy manifold in these R directions:

[0148]

[0149] Step D3: Project the noisy manifold Y onto the R directions obtained in step D2 to obtain the manifold G of the true signal. The true signal g(kT) can be recovered by averaging the anti-diagonal aspects of the true signal manifold G. d ).

[0150] A noise suppression scheme based on a weak measurement sensing system, characterized in that it includes:

[0151] Module M1: Constructs a quantum weak measurement optical platform. Without introducing the parameter to be measured during the weak coupling process, it performs preliminary measurements on the system and obtains the power spectrum S of the coupling noise based on the system output. N (f).

[0152] Module M2: Introduces the parameter to be measured during the weak coupling process, measures the system, and obtains the system output y(kT) which is a mixture of the parameter to be measured g(t) and the coupling noise n(t). d ), k = 1, 2, ...

[0153] Module M3: Outputs y(kT) from the system d Calculate its power spectrum S Y (f) and retain phase information from S Y (f) Subtracting the noise power spectrum S N (f) Combining the retained phase information, the spectrum of the recovered true signal can be obtained. The true signal can be recovered by performing an inverse Fourier transform on the recovered spectrum.

[0154] Module M4: For the real signal recovered from step 3, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise.

[0155] Preferably, the module M1 includes:

[0156] Module M1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during the weak coupling process, generating a time-varying phase parameter n(t). After interaction, the state of the output light is...

[0157] Module M1.2: The post-selection state is modulated as |f(t)>, and the weakly coupled light is projected onto the post-selection state. The state of the output light after projection is represented as |φ. f (t)>= <f|Φ i >. Based on the required detection frequency f, the two post-selective modulations are as follows: as well as

[0158] Module M1.3: Uses the center frequency of photons as the detection index. If a spectrometer is used for detection, and the detection time of the spectrometer is T, then the output of the spectrometer is: It can collect data for as long as possible to achieve high-precision estimation of noise power spectrum.

[0159] Module M1.4: Two spectrometer outputs corresponding to the post-selection states |f1(t)> and |f2(t)>. <p f > T We can calculate them separately. as well as Since we know the real and imaginary parts of the spectrum of the noise at frequency f, we can further calculate the spectrum of the noise at frequency f. The power spectrum of noise can be calculated using Wiener-Khinchin's theorem:

[0160] Preferably, module M2 includes: using a general weak amplification scheme, such as standard weak amplification or bias weak amplification, to introduce the time-varying parameter g(t) to be measured during the interaction process, and obtain the noisy system output y(kT). d ), k = 1, 2, ...

[0161] Preferably, the module M3 includes: assuming the system output y(kT) d The relationship between y(kT) and the real signal g(t) and noise n(t) is given by y(kT) d )=g(kT d )+n(kT d Since the real signal and noise are uncorrelated, and the noise is a zero-mean stationary process, we have |G(ω)| 2 =E[|Y(ω)| 2 ]-S N (ω). If the autocorrelation function of the noise satisfies ergodicity, then we can obtain And assume Φ X (ω)≈Φ Y (ω), therefore Performing an inverse Fourier transform will recover g(kT)d ).

[0162] Preferably, module M4 includes: when the data denoised by module M3 still contains noise,

[0163] Module M4.1: Select the embedding dimension L, and denoise the time series y(kT) after module M3. d Embedded into its L-dimensional phase space, generating a noisy manifold Y in the phase space.

[0164]

[0165] Module M4.2: Select sub-dimension R, and select R mutually orthogonal directions (u1, u2, ..., u3) in the phase space. R This maximizes the energy, i.e., the variance, of the noisy manifold in these R directions:

[0166]

[0167] Module M4.3: Project the noisy manifold Y onto the R directions obtained from module M4.2 to obtain the manifold G of the true signal. The true signal g(kT) can be recovered by averaging the anti-diagonal aspects of the true signal manifold G. d ).

[0168] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0169] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A noise suppression method based on a weak measurement sensing system, characterized in that, include: Step S1: Construct a quantum weak measurement optical platform. Without introducing the parameter to be measured during the weak coupling process, perform preliminary measurements on the system and obtain the power spectrum of the coupling noise based on the system output. Step S2: Introduce the parameter to be measured during the weak coupling process, measure the system, and obtain the system output that is a mixture of the parameter to be measured and the coupling noise; Step S3: Calculate the power spectrum of the system output and retain the phase information. Subtract the noise power spectrum from the system output power spectrum. Combine the retained phase information to obtain the recovered true signal spectrum. Perform an inverse Fourier transform on the recovered spectrum to recover the true signal. Step S4: For the recovered real signal, determine whether there is residual noise. If so, it is residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise. In step S1: Step S1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during weak coupling, resulting in time-varying phase parameters. After the interaction, the output light is in the following state: ; in, This represents the input state of the system, i.e., the polarization state of the photon. This represents the interaction between the system and the pointer. , This indicates the angular frequency of the photon. For time, It is random coupling noise introduced during the interaction process; Step S1.2: Modulate the post-selected state to The light after weak coupling is projected onto the post-selected state, and the state of the output light after projection is represented as follows: ; the frequency to be detected as needed Two-way post-selective modulation is as well as ; Step S1.3: Use the center frequency of the photon as the detection index. The detection was performed using a spectrometer, and the spectrometer detection time was... The spectrometer output is ; in, The momentum operator is the angular frequency of the photon. This is the start time of the measurement. for The energy of the output light collected within a time period; Step S1.4: Corresponding to the post-selection state and Two-channel spectrometer output Calculate respectively as well as This corresponds to the noise frequency at this time. The real and imaginary parts of the spectrum; in, express Noise over time The rest of the time is 0. for The energy of the output light collected within a time period, for The center frequency of the output light collected within the time period, The luminous efficiency of the light source. The center frequency of the light source; Calculate the frequency corresponding to the noise Spectrum The power spectrum of the noise was calculated using Wiener-Khinchin's theorem. .

2. The noise suppression method based on a weak measurement sensing system according to claim 1, characterized in that, In step S2: Weak value amplification schemes, including standard weak value amplification or bias weak value amplification, are used to introduce the time-varying parameter to be measured during the interaction process. Obtain the noisy system output , This refers to the data sampling period.

3. The noise suppression method based on a weak measurement sensing system according to claim 1, characterized in that, In step S3: System output With real signals and noise The relationship between them is The real signal and noise are uncorrelated, and the noise is a zero-mean stationary process. ;in, The spectrum of the real signal. The spectrum of the noisy signal. The power spectrum of the noise. This represents the statistical mean; if the autocorrelation function of the noise satisfies ergodicity, then we obtain... ; , Perform inverse Fourier transform to recover ; in, The phase spectrum of the real signal. This represents the phase spectrum of the noisy signal.

4. The noise suppression method based on a weak measurement sensing system according to claim 1, characterized in that, In step S4: Step S4.1: Select the embedding dimension Denoising the time series Embedded into it A 3D phase space is used to generate noisy manifolds in the phase space. : ； in, Indicates For the embedding dimension, the phase points are embedded into the phase space. This indicates the number of phase points embedded in the phase space; Step S4.2: Select sub-dimensions Select the phase space A mutually orthogonal direction This makes the noisy manifold in this The energy variance is largest in each direction: in, Let be the subscript of the direction of the feature being sought. For phase points embedded into phase space; Step S4.3: Transform the noisy manifold The information obtained in step S4.2 Manifolds that project the real signal in each direction For the real signal manifold Anti-diagonal average recovers the true signal .

5. A noise suppression system based on a weak measurement sensing system, characterized in that, include: Module M1: Constructs a quantum weak measurement optical platform, which does not introduce the parameter to be measured during the weak coupling process, performs preliminary measurements on the system, and obtains the power spectrum of the coupling noise based on the system output; Module M2: Introduces the parameter to be measured during the weak coupling process, measures the system, and obtains the system output that is a mixture of the parameter to be measured and the coupling noise; Module M3: Calculates the power spectrum of the system output and retains the phase information. Subtracts the noise power spectrum from the system output power spectrum and combines it with the retained phase information to obtain the recovered true signal spectrum. Performs an inverse Fourier transform on the recovered spectrum to recover the true signal. Module M4: For the recovered real signal, determine whether there is residual noise. If so, it indicates residual non-stationary noise. Use singular spectrum analysis to eliminate the residual non-stationary noise. In module M1: Module M1.1: Photons emitted from the light source are modulated into a pre-selected state. Noise is introduced during weak coupling, resulting in time-varying phase parameters. After the interaction, the output light is in the following state: ; in, This represents the input state of the system, i.e., the polarization state of the photon. This represents the interaction between the system and the pointer. , This indicates the angular frequency of the photon. For time, It is random coupling noise introduced during the interaction process; Module M1.2: Post-selection state modulation is The light after weak coupling is projected onto the post-selected state, and the state of the output light after projection is represented as follows: ; the frequency to be detected as needed Two-way post-selective modulation is as well as ; Module M1.3: Uses the center frequency of photons as the detection index. The detection was performed using a spectrometer, and the spectrometer detection time was... The spectrometer output is ; in, The momentum operator is the angular frequency of the photon. This is the start time of the measurement. for The energy of the output light collected within a time period; Module M1.4: Corresponds to the post-selection state and Two-channel spectrometer output Calculate respectively as well as This corresponds to the noise frequency at this time. The real and imaginary parts of the spectrum; in, express Noise over time The rest of the time is 0. for The energy of the output light collected within a time period, for The center frequency of the output light collected within the time period, The luminous efficiency of the light source. The center frequency of the light source; Calculate the frequency corresponding to the noise Spectrum The power spectrum of the noise can be calculated using Wiener-Khinchin's theorem. .

6. The noise suppression system based on a weak measurement sensing system according to claim 5, characterized in that, In module M2: Weak value amplification schemes, including standard weak value amplification or bias weak value amplification, are used to introduce the time-varying parameter to be measured during the interaction process. Obtain the noisy system output , This refers to the data sampling period.

7. The noise suppression system based on a weak measurement sensing system according to claim 5, characterized in that, In module M3: System output With real signals and noise The relationship between them is The real signal and noise are uncorrelated, and the noise is a zero-mean stationary process. ;in, The spectrum of the real signal. The spectrum of the noisy signal. The power spectrum of the noise. This represents the statistical mean; if the autocorrelation function of the noise satisfies ergodicity, then we obtain... ; , Perform inverse Fourier transform to recover ; in, The phase spectrum of the real signal. This represents the phase spectrum of the noisy signal.

8. The noise suppression system based on a weak measurement sensing system according to claim 5, characterized in that, In module M4: Module M4.1: Selecting the Embedding Dimension Denoising the time series Embedded into it A 3D phase space is used to generate noisy manifolds in the phase space. : ； in, Indicates For the embedding dimension, the phase points are embedded into the phase space. This indicates the number of phase points embedded in the phase space; Module M4.2: Selecting Sub-dimensions Select the phase space A mutually orthogonal direction This makes the noisy manifold in this The energy variance is largest in each direction: in, Let be the subscript of the direction of the feature being sought. For phase points embedded into phase space; Module M4.3: Transforms noisy manifolds Obtained from module M4.2 Manifolds that project the real signal in each direction For the real signal manifold Anti-diagonal average recovers the true signal .

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