A quantum illumination method based on non-gaussian two-mode entangled state

Abstract

The present application belongs to the field of quantum technology, and discloses a quantum illumination method based on a non-Gaussian two-mode entangled state in the field of quantum illumination, which comprises preparing a non-Gaussian two-mode entangled state, dividing it into two modes of light, one of which is signal mode light and the other is idle frequency mode light, emitting the signal mode light to the area of a potential target, directly emitting the idle frequency mode light to a measurement end, and finally measuring the reflected mode light of the potential target area and the idle frequency mode light at a receiver. The measurement scheme used in the present application uses double homodyne detection measurement. The present application has the following important advantages: 1. By improving the input state to a non-Gaussian two-mode entangled state, the value of quantum Fisher information can be effectively improved; 2. By using double homodyne detectors at the measurement end, the signal-to-noise ratio in the quantum illumination system can be effectively improved and error propagation can be reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of quantum, and relates to quantum illumination technology, in particular to a quantum illumination method based on a non-Gaussian two-mode entangled state. BACKGROUND

[0002] Quantum illumination provides a reliable help for modern object detection. The concept of quantum illumination is first proposed by S. Lloyd, which is to illuminate a target area with entangled signals and then measure the reflected light. Surprisingly, even if the entanglement itself cannot survive, the remaining correlation between the two initially entangled systems is still much higher than that provided by any initial classical state; the results show that the use of entangled states can improve the possibility of target detection. Although quantum illumination improves the accuracy of detecting objects in theory, there is still a lot of room for development in terms of quantum Fisher information and signal-to-noise ratio.

[0003] After Lloyd proposed quantum illumination, researchers used two-mode squeezed entangled states in the input state, and also used asymmetrically squeezed two-mode states and super-entangled states in combination with quantum illumination. Similarly, at the measurement end, there are many different measurement schemes, such as optical parametric amplification measurement, phase conjugation measurement, etc. However, the above measurement methods combined with the proposed quantum input state show a low signal-to-noise ratio of quantum illumination. At the same time, because it is a nonlinear structure, the experimental structure is also very complex. SUMMARY

[0004] To solve the above technical problems, the application provides a quantum illumination method based on a non-Gaussian two-mode entangled state, which can effectively improve the measurement accuracy of quantum illumination.

[0005] The quantum illumination method based on a non-Gaussian two-mode entangled state provided by the application has the following steps:

[0006] S1: preparing a non-Gaussian two-mode entangled state, which is prepared based on a two-mode squeezed vacuum entangled state; the non-Gaussian two-mode entangled state has two states: one is obtained by photon extraction of the two-mode squeezed vacuum entangled state through a beam splitter to obtain a photon-extracted non-Gaussian two-mode entangled state; the other is obtained by photon addition of the two-mode squeezed vacuum entangled state through a parametric amplifier to obtain a photon-added non-Gaussian two-mode entangled state;

[0007] S2: sending the prepared non-Gaussian two-mode entangled state;

[0008] S3: the prepared non-Gaussian two-mode entangled state is emitted in two ways, one of which is emitted to a target potential area, and this is called signal mode light;

[0009] S4: The measurement end accepts the reflected mode light reflected by the target potential area;

[0010] S5: The prepared non-Gaussian two-mode entangled state is directly emitted to the measurement end as idler mode light;

[0011] S6: The measurement end performs double homodyne detection measurement on the reflected light and the idler mode light.

[0012] Further, in step S1, the non-Gaussian two-mode entangled state has two forms:

[0013] The quantum state form of photon number extraction is The quantum state form of photon number increase is Where Dn is a coefficient, n represents the number of photons, subscript S represents signal mode, subscript I represents idler mode, and l represents extraction (or increase) of l photons in signal mode light and idler mode light.

[0014] Further, in step S3, the signal mode light is emitted into the target potential area, and if there is an object in the potential area, the target object is regarded as a 50:50 beam splitter with a reflection coefficient η.

[0015] Further, in step S3, whether the non-Gaussian two-mode entangled state has better performance than other known input states is determined by the size of quantum Fisher information; for example, the general two-mode Schmidt canonical form The quantum Fisher information solving process is as follows:

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[0029] The above is a general process for calculating quantum Fisher information, wherein the process for calculating quantum Fisher information needs to analogize the reflection coefficient of the beam splitter to 0, N B represents the number of environmental noise photons,

[0030] <ω α′ |s|ω α represents the operation on the signal mode light.

[0031] Further, in step S6, the double zero difference measurement is specifically implemented by using a 50:50 beam splitter to receive the reflected mode light and the idler mode light, and to divide the light into two paths, one of which is emitted to the 50:50 beam splitter with the local oscillator of θ = 0, and is measured at the output end by two intensity detectors, and the other is emitted to the 50:50 beam splitter with the local oscillator of Further, in step S6, the double zero difference measurement is specifically implemented by using a 50:50 beam splitter to receive the reflected mode light and the idler mode light, and to divide the light into two paths, one of which is emitted to the 50:50 beam splitter with the local oscillator of θ = 0, and is measured at the output end by two intensity detectors, and the other is emitted to the 50:50 beam splitter with the local oscillator of

[0032] Further, after the measurement in step S6, the error propagation coefficient and the signal-to-noise ratio are used to judge the goodness of the measurement scheme;

[0033] The formula of the error propagation coefficient is: wherein

[0034] <Mη>＝Tr ( MηρSIB ), is the variance of the measurement operator, <M η > is the mean value of the measurement operator, is the partial derivative of the measurement operator;

[0035] The formula of the signal-to-noise ratio is: wherein <M η > ＝ T r (M ηρSIB ) ，

[0036] <m0>=<M η＝0 >, Δη is the error propagation coefficient, SNR is the signal-to-noise ratio, is the variance of the measurement operator, <M η > is the mean value of the measurement operator.

[0037] Further, the measurement in the step S6 is generally photon number difference measurement, which is suitable for most input states, but the non-Gaussian two-mode entangled state used in the present application is not suitable, because if photon number difference measurement <M η > = 0 is used, the signal-to-noise ratio obtained is 0 regardless of whether the target object exists, and the advantage of the input state for quantum illumination cannot be compared, so the present application uses double zero difference measurement. The formula of double zero difference measurement is: Where a R represents the annihilation operator of the reflected mode light, represents the creation operator of the reflected mode light, aI represents the annihilation operator of the idler mode light, represents the creation operator of the idler mode light.

[0038] The beneficial effects of the present application are that, compared with the prior art, the two-mode squeezed state extracted by input photons and the two-mode squeezed state with increased photon number in the present application improve the quantum Fisher information and improve the accuracy of measuring the target object. At the measurement end, by comparing the non-Gaussian two-mode entangled state in the present application with the commonly used two-mode squeezed state in terms of signal-to-noise ratio and error propagation coefficient, it is found that the signal-to-noise ratio of the non-Gaussian two-mode entangled state is higher than that of the two-mode entangled state, and the error propagation coefficient is lower than that of the two-mode entangled state, which reflects the advantage of the non-Gaussian two-mode entangled state. The double zero difference detection in the present application is completed using linear optical devices, which can be realized by the prior art, and the practicability is improved. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is the communication flowchart of the method of the present application;

[0040] Figure 2 is the schematic diagram of the principle of quantum illumination of the method of the present application;

[0041] Figure 3 is the double zero difference measurement schematic diagram of the method of the present application. DETAILED DESCRIPTION

[0042] In order to make the content of the present application more easily and clearly understood, the present application will be further described in detail below according to specific embodiments and in conjunction with the drawings.

[0043] As Figure 1 shown, the present application provides a quantum illumination method based on a non-Gaussian two-mode entangled state. It comprises the following steps:

[0044] S1: First, a non-Gaussian two-mode entangled state is prepared. The non-Gaussian entangled state is based on a two-mode squeezed vacuum entangled state. The non-Gaussian two-mode entangled state can be divided into two states: one is a photon-dropped non-Gaussian two-mode entangled state obtained by photon extraction from the two-mode squeezed vacuum entangled state; the other is a photon-added non-Gaussian two-mode entangled state obtained by photon addition to the two-mode squeezed vacuum entangled state. The quantum state representation of photon extraction is as follows: The quantum state with an increased number of photons is characterized by the following: Where l represents the extraction (addition) of l photons in both signal light mode and idle light mode.

[0045] S2: Send the prepared non-Gaussian entangled state.

[0046] S3: As Figure 2 The prepared non-Gaussian entangled state is emitted in two paths. One path, called the signal mode light, is emitted into the target potential region. If an object exists in the potential region, the target object can be considered a 50:50 beam splitter with a reflection coefficient of η. Whether the non-Gaussian two-mode entangled state performs better than other known input states is determined by the magnitude of the quantum Fisher information. (Quantum state extracted by photon number) For example, where N = nl, and l is the number of photons extracted, the quantum Fisher information solution process is as follows:

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[0052] The above describes the general process for calculating quantum Fisher information. This process requires that the reflection coefficient of the beam splitter, analogous to the target object, be approached to 0. B This represents the number of photons in the ambient noise.

[0053] S4: The measuring end receives the reflected light pattern obtained from the reflection of the target's potential region. The target object can then be considered as a 50:50 beam splitter with a reflection coefficient of η. The expression of the input state after reflection is:

[0054] S5: The prepared non-Gaussian entangled state will be directly emitted to the measurement end; this path is called the idler mode light.

[0055] S6: The measurement end performs dual-zero-difference detection measurements on both the reflected mode light and the idler mode light. The specific implementation of the dual-zero-difference measurement is... Figure 3 As shown, a 50:50 beam splitter receives the reflected mode light and the idler mode light, splitting them into two paths. One path, along with a local oscillator at θ=0, is emitted onto the 50:50 beam splitter, and its output is measured by two intensity detectors. The other path is... The local oscillator transmits the signal to a 50:50 beam splitter, and two intensity detectors are used at the output for measurement. The measurement operator for the dual null difference measurement is: in Where aR represents the annihilation operator for reflected mode light. aI represents the operator for generating reflected mode light, and aI represents the operator for annihilating idler mode light. Operator for generating idler mode light.

[0056] The quality of a measurement scheme is judged by its error propagation coefficient and signal-to-noise ratio. The formula for the error propagation coefficient is: in: <M η >=Tr(M η ρ SIB ), It is the variance of the measurement operator. <M η > is the mean of the measurement operators. This involves taking the partial derivative with respect to the measurement operator. The formula for signal-to-noise ratio is: The signal-to-noise ratio can also be rewritten using the error propagation coefficient:

[0057] in: <M η >=Tr(M η ρ SIB ), <m0>= <M η＝0 >, Δη is the error propagation coefficient, SNR is the signal-to-noise ratio, is the variance of the measurement operator, <M η > is the mean of the measurement operator, is the partial derivative of the measurement operator. Solving the signal-to-noise ratio and the error propagation coefficient is to calculate <M η > and

[0058] <M η > = Tr (M η ρ SIB )

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[0065] According to the above expression, the corresponding signal-to-noise ratio and error propagation coefficient can be obtained by substituting the coefficients of the input state. The non-Gaussian two-mode entangled state of photon number extraction and the non-Gaussian two-mode entangled state of photon number increase are the same solving process. Finally, the signal-to-noise ratio and the error propagation coefficient are simulated by Mathematica to obtain the corresponding results.

[0066] The above only describes the preferred scheme of the present application, and is not intended to further limit the present application, and any equivalent changes made according to the content of the present application and the drawings are within the scope of protection of the present application.

Claims

1. A quantum illumination method based on non-Gaussian two-mode entangled states, characterized in that, The steps of the method are: S1: preparing a non-Gaussian two-mode entangled state, which is prepared based on a two-mode squeezed vacuum entangled state; the non-Gaussian two-mode entangled state has two states: one is obtained by photon extraction of the two-mode squeezed vacuum entangled state through a beam splitter; the other is obtained by photon addition of the two-mode squeezed vacuum entangled state through a parametric amplifier; S2: sending the prepared non-Gaussian two-mode entangled state; S3: the prepared non-Gaussian two-mode entangled state is emitted in two ways, one of which is emitted to the target potential area, and this is called signal mode light; S4: the measurement end receives the reflected mode light reflected by the target potential area; S5: the other way of the prepared non-Gaussian two-mode entangled state is directly emitted to the measurement end, which is called idler mode light; S6: the measurement end performs double zero difference detection measurement on the reflected light and the idler mode light, and judges the measurement method; Wherein, the double zero difference measurement is realized by using a 50:50 beam splitter to accept the reflected mode light and the idler mode light, which are divided into two paths, one of which is emitted to the 50:50 beam splitter with the local oscillator with θ=0, and is measured at the output end by two intensity detectors, and the other is emitted to the 50:50 beam splitter with the local oscillator with θ=π / 2, and is also measured at the output end by two intensity detectors. Wherein, the double zero difference measurement is realized by using a 50:50 beam splitter to accept the reflected mode light and the idler mode light, which are divided into two paths, one of which is emitted to the 50:50 beam splitter with the local oscillator with θ=0, and is measured at the output end by two intensity detectors, and the other is emitted to the 50:50 beam splitter with the local oscillator with θ=π / 2, and is also measured at the output end by two intensity detectors. The two-zero difference measurement formula is: where a R represents an annihilation operator of the reflected mode light, represents a creation operator of the reflected mode light, represents an annihilation operator of the idler mode light, represents a creation operator of the idler mode light.

2. The quantum illumination method based on non-Gaussian two-mode entangled states according to claim 1, wherein, In step S1, the non-Gaussian two-mode entangled state has two forms: The quantum state representation of the photon number subtraction is The quantum state representation of the photon number addition is where Dn is a coefficient, n represents the photon number, the subscript S represents a signal mode, and the subscript I represents an idler mode, represents that the signal mode light and the idler mode light change one photon.

3. The quantum illumination method based on non-Gaussian two-mode entangled states according to claim 1, wherein, In step S3, the signal mode light is emitted into the target potential area, and if there is an object in the potential area, the target object is regarded as a 50:50 beam splitter with a reflection coefficient η.

4. The quantum illumination method based on non-Gaussian two-mode entangled states according to claim 1, wherein, In step S3, whether the non-Gaussian two-mode entangled state has better performance than other known input states is determined by the size of the quantum Fisher information.

5. The quantum illumination method based on non-Gaussian two-mode entangled states according to claim 1, wherein, After step S6, the error propagation coefficient and the signal-to-noise ratio are used to judge the good and bad of the measurement scheme; The formula for the error propagation coefficient is: where η η SIB is the variance of the measurement operator, <M η > is the mean of the measurement operator, is the partial derivative with respect to the measurement operator;​​​​ The formula for the signal-to-noise ratio is: where <M η > = Tr(M η ρ SIB ), <m0>= <M η＝0 >, is the variance of the measurement operator, <M η > is the mean of the measurement operator.

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