A quantum precision measurement method based on photon number coherent superposition state

Abstract

The present invention relates to the field of quantum precision measurement technology, and in particular to a quantum precision measurement method based on a coherent superposition state of photon numbers. The advantage of this method is that the Wigner function of the coherent superposition state of photon numbers has a fine structural distribution in both the radial and tangential directions, which can be used to measure the displacement variable and phase variable of the light field, respectively; and as the number of photons N increases, the distribution of its Wigner function in different directions becomes increasingly fine, which can achieve quantum precision measurement close to the Heisenberg limit. The measurement steps for the displacement variable include: preparing a coherent superposition state of photon numbers as a detection state in a quantum system; using the detection state to detect the displacement variable of the light field, measuring a physical quantity of the quantum state after the detection process, and inferring the information of the displacement variable to be measured through the measurement results; specifically, this scheme designs two different measurement schemes: measuring the probability of the distribution of the number of photons in the quantum state and measuring the parity of the photon number.

Description

Technical Field

[0001] The present invention relates to the field of quantum precision measurement technology, and in particular to a quantum precision measurement method based on coherent superposition states of photon numbers. Background Art

[0002] Quantum precision measurement aims to leverage quantum resources and effects to achieve measurement accuracy exceeding that of classical methods. It is one of the most important applications of quantum information. To improve measurement accuracy, classical measurement requires both the preparation and utilization of a "ruler" with higher resolution and the ability to repeat measurements under identical conditions to obtain an average result. The fluctuations in these measurement results are at least proportional to the proportionality factor 1 / √M (where M is the number of repeated measurements). This is the standard quantum limit, a proven limit that cannot be broken by classical repeated measurement methods.

[0003] In pursuit of higher measurement accuracy, researchers have combined classical statistics with quantum mechanics, a method known as quantum precision measurement. Quantum precision measurement, which leverages quantum effects or quantum system design schemes to estimate parameters, can surpass the standard quantum limit. By exploiting the Heisenberg uncertainty principle, a fundamental property of quantum mechanics, the maximum precision achievable through quantum precision measurement theory is capped at 1 / N (where N is a positive integer representing the number of particles or excitations in the probe state), known as the Heisenberg limit. As the number of particles or excitations in the probe state, N, increases, the achievable precision of the precision measurement increases. Reaching the Heisenberg limit requires quantum measurement processes that generally involve two approaches: preparing specialized non-singular probe states or designing specialized measurement interactions. Non-singular probe states can be entangled states of multiple particles, squeezed states, or Bose modes in an infinite-dimensional Hilbert space. Regarding multi-particle entangled states as probe states, there have been reports of quantum precision measurements using entangled states such as GHZ (Greenberger-Horne-Zeilinger) entangled states, NOON states, and spin-squeezed states. However, increasing the number of entangled particles and improving their fidelity are significant challenges in each physical system. Therefore, the accuracy of such precision measurements is limited by the number of entangled particles and their fidelity. Precision measurements using squeezed vacuum states as probe states successfully detected gravitational waves generated by the collision of two black holes 13 billion light-years away in 2015. Further improvements in the squeezing of such probe states also face significant challenges. In comparison, single Bose modes have enormous potential for quantum precision measurements because they inherently possess infinite-dimensional Hilbert space, and the nonclassical quantum states of multiple Bose modes have a finely structured distribution. However, the number of quantum state excitations of existing Bose modes used for precision measurements is still relatively low, limiting the accuracy of achievable quantum precision measurements. Furthermore, the quantum state of existing solutions can only measure a single quantity to be measured, and is not applicable to systems with multiple quantities to be measured. Therefore, existing technologies need to be improved and developed. Summary of the Invention

[0004] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide a quantum precision measurement method based on the coherent superposition state of photon numbers, aiming to solve the problem in existing quantum precision measurement that one detection state can only measure one thing to be measured, and the problem that the measurement accuracy is limited by the number of quantum resource excitations, resulting in low measurement accuracy.

[0005] The technical solutions of the present invention are as follows:

[0006] A quantum precision measurement method based on photon number coherent superposition state comprises the following steps:

[0007] Design and construct quantum systems containing Bose modes to prepare photon number coherent superposition states As the detection state, where N is a positive integer;

[0008] The detection state is used to detect the light field displacement variable, and a physical quantity of the quantum state after the detection process is measured, and the information of the displacement variable to be measured is further inferred from the measurement result.

[0009] The present invention designs two different measurement schemes, including the measurement of the probability of the quantum state photon number distribution and the measurement of the quantum state photon number parity. Both of these measurement schemes can be used to infer the information of the displacement variable to be measured.

[0010] The quantum precision measurement method based on the coherent superposition state of photon numbers, wherein the quantum system includes:

[0011] Linear Bose mode resonant cavity, used for preparation of detection state and detection of displacement variables;

[0012] Nonlinear quantum bits, used to assist in the preparation of detection states and the measurement of physical quantities;

[0013] Read resonant cavity, used to read the quantum bit state;

[0014] The nonlinear quantum bit is coupled to the linear Bose mode resonant cavity and the readout resonant cavity respectively to realize the manipulation and measurement of various quantum states.

[0015] The quantum precision measurement method based on the coherent superposition state of photon numbers, wherein the coherent lifetime of the Bose mode in the linear resonant cavity is more than 1 millisecond.

[0016] The quantum precision measurement method based on the coherent superposition state of photon numbers, wherein the detection state is prepared with the assistance of nonlinear quantum bits, and when N in the prepared detection state is no more than 20, the preparation fidelity is no less than 96%.

[0017] In the aforementioned quantum precision measurement method based on photon number coherent superposition states, the displacement variable to be measured can be determined using two methods. First, the photon number distribution probability of the quantum state after the detection process can be measured; second, the photon number parity of the quantum state after the detection process can be measured. Both measurement schemes can further infer the measurement results to obtain the displacement variable to be measured.

[0018] The quantum precision measurement method based on the coherent superposition state of photon numbers, wherein the step of determining the displacement variable to be measured by the photon number distribution probability of the quantum state comprises: using the selective waveform of the nonlinear quantum bit to measure the photon number distribution probability of the quantum state at |0> and |N> respectively, and the relationship between the photon number distribution probability of the quantum state at |0> and |N> and the displacement variable to be measured is respectively and Among them, β represents the displacement variable to be measured, L N represents the Laguerre polynomial; then the relationship between the sum of the probability of the photon number distribution at the two locations and β satisfies: Therefore, the measured P 0+N The size of the displacement variable to be measured can be inferred in reverse. Furthermore, the displacement accuracy determined by the measurement scheme can be obtained. The classical Fisher information of the sum of the probability of the photon number distribution of the quantum state in |0> and |N> is The displacement accuracy is

[0019] The quantum precision measurement method based on the coherent superposition state of photon numbers, wherein the specific steps of the quantum state photon number parity measurement scheme include: using the gradient ascent algorithm to prepare the entangled state of the linear Bose mode photon number parity and the nonlinear quantum bit state in the resonant cavity, and realizing the measurement of the quantum state photon number parity by measuring the quantum bit state. The photon number parity distribution of the quantum state after translation is equivalent to the Wigner function distribution, and the relationship between the Wigner function distribution and the displacement variable to be measured satisfies Among them, β represents the displacement to be measured, L N represents the Laguerre polynomial; the Wigner function distribution in the measurement is the probability distribution P of the nonlinear quantum bit in the ground state g Get, P g With W 0+N The relationship between them satisfies P g =(W 0+N +1) / 2; further, the displacement accuracy determined by the measurement scheme can be obtained, and the classical Fisher information of the photon number parity distribution of the quantum state after translation is The displacement accuracy is

[0020] Beneficial effect: The present invention provides a quantum precision measurement method based on the coherent superposition state of photon numbers, comprising the steps of: designing and constructing a quantum system including Bose modes and quantum bits, preparing the coherent superposition state of photon numbers, As a detection state, where N is a positive integer; the detection state is used to detect the light field displacement variable, and a physical quantity of the quantum state after the detection process is measured, and information about the displacement variable to be measured is inferred from the change in the physical quantity; specifically, two different measurement schemes are designed, including measurement of the probability of the quantum state photon number distribution and measurement of the quantum state photon number parity, both of which can be used to infer the displacement variable to be measured. The present invention uses a photon number coherent superposition state as a detection state. In phase space, the Wigner function of the photon number coherent superposition state has a fine structure distribution in the radial and tangential directions, which can be used to respectively realize the measurement of the light field displacement variable and the phase variable. It is a quantum precision measurement detection state that can be used for the measurement of multiple variables, laying the foundation for simultaneous quantum precision measurement of multiple variables. Moreover, as the number of photons N increases, the distribution of its Wigner function in different directions becomes more and more refined, so quantum precision measurement of different variables close to the Heisenberg limit can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Wigner function images for experimental preparation and ideal detection states;

[0022] Figure 2 Schematic diagram of quantum system;

[0023] Figure 3 Schematic diagram of the circuit for measuring the probability of the number distribution of photons in a quantum state;

[0024] Figure 4 This is a schematic diagram of the circuit for measuring the parity of quantum state photon numbers;

[0025] Figure 5 This is a curve diagram of displacement accuracy results obtained using the photon number distribution probability measurement method;

[0026] Figure 6 This is a curve diagram of the displacement accuracy results obtained using the photon number parity measurement method. DETAILED DESCRIPTION

[0027] The present invention provides a quantum precision measurement method based on the coherent superposition of photon numbers. To clarify the objectives, technical solutions, and effects of the present invention, the present invention is described in further detail below. It should be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention.

[0028] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0029] Since this detection state has been proven to be able to be used for precise measurement of light field phase variables, the present invention further proves that this detection state can be used for quantum precision measurement of light field displacement variables, thereby proving that this quantum state can be used for quantum precision measurement of a variety of quantities to be measured, and by increasing the number of excitations of the detection state, the measurement accuracy is improved.

[0030] Based on this, the present invention provides a quantum precision measurement method based on the coherent superposition state of photon numbers, comprising the steps of:

[0031] Step S10: Design and construct a quantum system containing Bose modes and auxiliary quantum bits to prepare a photon number coherent superposition state As the detection state, where N is a positive integer;

[0032] Step S20: Utilize the detection state to detect the light field displacement variable, measure a physical quantity of the quantum state after the detection process, and infer information about the displacement variable to be measured through the measurement result.

[0033] In this embodiment, the photon number coherent superposition state is used As a detection state, in the phase space, this quantum state has fine structural distribution in the radial and tangential directions, which can be used to realize the measurement of light field displacement variables and light field phase variables respectively. It is a quantum state that can be used to measure different physical quantities; and as the number of photons N increases, the distribution of its Wigner function in different directions becomes more and more fine, so quantum precision measurement close to the Heisenberg limit can be achieved. This method is a quantum precision measurement close to the Heisenberg limit that can realize different variables, laying the foundation for simultaneous quantum precision measurement of multiple variables. Specifically, the present invention designs and processes a quantum system including superconducting quantum bits and high-quality superconducting resonant cavities; uses superconducting quantum bits as auxiliary bits to assist in the preparation and measurement of detection states; prepares quantum states in high-quality superconducting resonant cavities as detection states for precision measurement, and the detection states have a long coherent lifetime; with the assistance of superconducting quantum bits, prepares coherent superposition states of different photon numbers. This is then used as a probe state to detect the light field displacement variable. A physical quantity in the quantum state after the detection process is measured, and information about the displacement variable to be measured is inferred from the measurement results. Furthermore, the present invention designs two different measurement schemes: measuring the probability of the quantum state photon number distribution and measuring the parity of the quantum state photon number distribution. Both measurement schemes can infer information about the displacement to be measured.

[0034] In some embodiments, in order to achieve the ultra-low temperature environment required for superconducting quantum bits, the quantum precision measurement method based on the coherent superposition state of photon numbers is carried out in a dilution refrigerator, and the lowest temperature in the temperature zone where the sample is located is less than 10mK, which ensures the superconducting properties of the sample and allows the superconducting quantum bit to be prepared in the ground state by cooling.

[0035] In some embodiments, the detection state is prepared using a gradient ascent pulse engineering (GRAPE) method in the linear superconducting resonant cavity with the assistance of a superconducting quantum bit. The detection state obtained by this system using this method has high fidelity.

[0036] Specifically, if Figure 1 As shown in the figure, high-fidelity coherent superposition states with different photon numbers are prepared in a linear superconducting resonant cavity using the gradient ascent algorithm. Take this as an example to demonstrate, Figure 1 The first row in is the Wigner image of the experimentally prepared probe state, Figure 1 The second line in is the Wigner image of the ideal detection state. Figure 1 As can be seen in the figure, the Wigner image of this quantum state has fine structures in both radial and tangential directions, which can be used to measure displacement variables and phase variables respectively. Therefore, the photon number coherent superposition state is a quantum state that can be used to measure different quantities. Since the linear superconducting resonant cavity has a high quality factor, the coherent lifetime of the Bose mode in the resonant cavity is more than 1 millisecond, so that a detection state with a higher excitation number N can be prepared to achieve higher measurement accuracy. Figure 1 It can be seen that the Wigner function distribution of the detection state has a finer distribution with the increase of the excitation number N, which can be used to achieve high-precision quantum precision measurement close to the Heisenberg limit.

[0037] In some embodiments, as Figure 2 As shown, the quantum system includes:

[0038] A linear Bose mode resonant cavity 10 in which the detection state can be prepared and the displacement variable can be detected;

[0039] Nonlinear quantum bit 20, used to assist in the preparation of detection states and the measurement of quantum state physical quantities;

[0040] A read resonant cavity 30 for reading the quantum bit state;

[0041] The nonlinear quantum bit 20 is coupled to the linear Bose mode resonant cavity 10 and the readout resonant cavity 30 respectively to achieve manipulation and measurement of various quantum states.

[0042] Specifically, the linear Bose mode resonant cavity 10 has a high quality factor, and the quantum state prepared therein It is used as a detection state for precision measurement and has a long coherent lifetime; the nonlinear quantum bit is used to assist in the preparation of the detection state and the measurement of quantum state physical quantities.

[0043] In some embodiments, the quantum system is made of ultra-high purity aluminum, with a purity of up to 99.999%.

[0044] In some embodiments, the detection state is prepared using a gradient ascent algorithm in the linear Bose mode resonant cavity with the assistance of a nonlinear quantum bit; when N is not greater than 20, the fidelity of the detection state preparation is not less than 96%.

[0045] In some embodiments, the maximum value of N in the experiment is 20. Theoretically, a larger N is better, thus achieving higher measurement accuracy. However, due to limitations such as the coherence time of the experimental system, a larger N leads to lower fidelity in quantum state preparation, and the gain achievable in precision measurement decreases. In some preferred embodiments, N = 8, 10, 12, 14, 16, 18, or 20, but is not limited thereto.

[0046] In some embodiments, the displacement variable to be measured can be obtained through two different measurement schemes; that is, the displacement variable to be measured is determined by the photon number distribution probability or photon number parity of the quantum state, and the displacement to be measured can be inferred through these two measurement schemes.

[0047] In some embodiments, the step of determining the displacement variable to be measured by the photon number distribution probability of the quantum state includes: Figure 3 As shown, the selective waveform of the nonlinear quantum bit is used to measure the probability of the photon number distribution of the quantum state in |0> and |N> respectively. The relationship between the probability of the photon number distribution of the quantum state in |0> and |N> and the measured displacement variable (β) is and PNβ=12e(-β2)LNβ22+1N!β2N; where β represents the displacement variable to be measured, L Nrepresents the Laguerre polynomial; then the relationship between the sum of the probability of the number of photons in the quantum state |0> and |N> and β satisfies According to the measured P 0+N The size of the displacement variable to be measured can be inferred in reverse. The classical Fisher information of the sum of the probability of the photon number distribution of the quantum state in |0> and |N> is Displacement accuracy meets Further analysis of the measurement data reveals the achievable measurement accuracy of this method, proving that the measurement accuracy of this scheme can approach the Heisenberg limit.

[0048] In some embodiments, the step of determining the displacement variable to be measured by the photon number parity of the quantum state includes: Figure 4 The waveform diagram shows the measurement of the displacement variable by measuring the photon number parity in the resonant cavity. The gradient ascent algorithm is used to prepare the entangled state of the Bose mode photon number parity and the nonlinear quantum bit state in the linear resonant cavity, thereby measuring the quantum bit state to achieve the measurement of the photon number parity of the quantum state after translation. The photon number parity distribution of the quantum state after translation is equivalent to the Wigner function distribution. The relationship between the Wigner function distribution and the displacement variable to be measured satisfies Where β represents the displacement to be measured, L N represents the Laguerre polynomial; the Wigner function distribution in the measurement is the probability distribution P of the nonlinear quantum bit in the ground state g Get, P g With W 0+N The relationship between them satisfies P g =(W 0+N +1) / 2; the classical Fisher information of the photon number parity distribution of the quantum state after translation is Displacement accuracy meets

[0049] Specifically, this embodiment provides two different measurement methods for characterizing the displacement to be measured: examining the probability distribution of the detected states |0> and |N>, or examining the photon number parity of the detected states to reflect the displacement to be measured. Both measurement methods achieve high accuracy, allowing flexibility in selecting the appropriate method based on practical needs. Using both the photon number distribution probability measurement and the photon number parity measurement for displacement measurement, the measurement accuracy approaches the Heisenberg limit, achieving precision measurement gains of 10.8dB and 11.1dB below the standard quantum limit at N = 20, respectively.

[0050] The present invention will be described in detail with reference to the following examples. It should also be understood that the following examples are only intended to further illustrate the present invention and are not to be construed as limiting the scope of protection of the present invention. Any non-essential improvements and adjustments made by those skilled in the art based on the above disclosure of the present invention fall within the scope of protection of the present invention.

[0051] Example 1

[0052] This embodiment obtains the size of the displacement variable by measuring the probability of the photon number distribution of the resonant cavity quantum state using the nonlinear quantum bits in the quantum system.

[0053] Take N=8, 10, 12, 14, 16, 18, 20 as an example, Figure 5 The graph shows the displacement accuracy curve obtained by measuring the detection states with N=8, 10, 12, 14, 16, 18, and 20, and the method of measuring the probability of the photon number distribution. The graph includes the standard quantum limit and the Heisenberg limit. The dots represent the displacement variable measurement accuracy obtained by using the superposition state of photons with different photon numbers as the detection state. The dotted line is its fitting curve. It can be seen that the experimental results (δβ∝N -0.48 ) approaches the Heisenberg limit and achieves a precision measurement gain of 10.8 dB below the standard quantum limit at N = 20.

[0054] Example 2

[0055] This embodiment obtains information on the displacement variable by performing photon number parity measurement of the resonant cavity quantum state using the nonlinear quantum bits in the quantum system.

[0056] Take N=8, 10, 12, 14, 16, 18, 20 as an example, Figure 6 The figure shows the displacement variable measurement accuracy obtained by using the method of photon number parity measurement with N = 8, 10, 12, 14, 16, 18, and 20 detection states; the figure includes the standard quantum limit and the Heisenberg limit, the dots represent the displacement variable measurement accuracy obtained by using the superposition state of photons with different photon numbers as the detection state, and the dotted line is its fitting curve. It can be seen that the experimental results (δβ∝N -0.47 ) approaches the Heisenberg limit and obtains a measurement gain of 11.1 dB below the standard quantum limit at N = 20.

[0057] Example 1 and Example 2 use two different measurement methods to prove that the coherent superposition state of different photon numbers can be used as a detection state to achieve higher precision measurement, and that the quantum state can be used to measure phase variables, so that the quantum state can simultaneously perform precise measurements of different physical quantities, laying the foundation for simultaneous precise measurement of multiple parameters.

[0058] In summary, the present invention provides a quantum precision measurement method based on the coherent superposition state of photon numbers, comprising the steps of: designing and constructing a quantum system including Bose modes and quantum bits, preparing the coherent superposition state of photon numbers, As a detection state, where N is a positive integer; the detection state is used to detect the light field displacement variable, and a physical quantity of the quantum state after the detection process is measured, and information about the displacement variable to be measured is inferred from the measurement results; and two different measurement schemes are designed, including a probability measurement of the quantum state photon number distribution and a measurement of the quantum state photon number parity, both of which can be used to infer the displacement variable to be measured. The present invention uses a photon number coherent superposition state as a detection state. In phase space, the Wigner function of the photon number coherent superposition state has a fine structure distribution in the radial and tangential directions, which can be used to respectively realize the measurement of the light field displacement variable and the phase variable. This is a quantum precision measurement method that can be used for the measurement of multiple variables, laying the foundation for simultaneous quantum precision measurement of multiple variables. Moreover, as the photon number N increases, the distribution of its Wigner function in different directions becomes increasingly fine, thus achieving quantum precision measurement of different variables close to the Heisenberg limit.

[0059] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A quantum precision measurement method based on the coherent superposition state of photon numbers, characterized in that: Including steps: Design and construct a quantum system containing Bose modes and auxiliary quantum bits to prepare photon number coherent superposition states As the detection state, where N is a positive integer; Utilizing the detection state to detect the light field displacement variable, measuring a physical quantity of the quantum state after the detection process, and inferring information about the displacement variable to be measured from the measurement result; The displacement variable to be measured is determined by the photon number distribution probability of the quantum state, and the steps include: using the selective waveform of the nonlinear quantum bit to respectively measure the quantum state in and The probability of the photon number distribution is measured, and the quantum state obtained by the measurement is and The size of the displacement variable to be measured can be inferred from the sum of the probability of the photon number distribution; Alternatively, the displacement variable to be measured is determined by the photon number parity of the quantum state, and the steps include: using a gradient ascent algorithm to prepare an entangled state of the photon number parity and the nonlinear quantum bit state in a linear resonant cavity, and measuring the photon number parity of the shifted quantum state by measuring the quantum bit state; in the measurement, the Wigner function distribution is obtained by the probability distribution of the nonlinear quantum bit in the ground state.

2. The quantum precision measurement method based on photon number coherent superposition state according to claim 1 is characterized in that: The quantum system comprises: Linear Bose mode resonant cavity, used for preparation of detection state and detection of displacement variables; Nonlinear quantum bits, used to assist in the preparation of detection states and the measurement of quantum state physical quantities; Read resonant cavity, used to read the quantum bit state; The nonlinear quantum bit is coupled to the linear Bose mode resonant cavity and the readout resonant cavity respectively to realize the manipulation and measurement of various quantum states.

3. The quantum precision measurement method based on photon number coherent superposition state according to claim 2 is characterized in that: The coherent lifetime of the Bose mode in the linear resonant cavity is longer than 1 millisecond.

4. The quantum precision measurement method based on photon number coherent superposition state according to claim 2 is characterized in that: The detection state is prepared with the assistance of a nonlinear quantum bit. When N in the prepared detection state is not greater than 20, the preparation fidelity is not less than 96%.

5. The quantum precision measurement method based on photon number coherent superposition state according to claim 1 is characterized in that: The quantum state is and The relationship between the photon number distribution probability and the displacement variable to be measured is and ;in, represents the displacement variable to be measured, Table Laguerre polynomials; The quantum state is and The sum of the photon number distribution probabilities is The relationship satisfies: , according to the measured Inversely deduce the size of the displacement variable to be measured; The quantum state after translation is and The classical Fisher information of the sum of the probability of the photon number distribution is , the displacement accuracy is .

6. The quantum precision measurement method based on photon number coherent superposition state according to claim 1 is characterized in that: The photon number parity distribution of the quantum state after translation is equivalent to the Wigner function distribution, and the relationship between the Wigner function distribution and the displacement variable to be measured satisfies ,in, represents the displacement to be measured, represents the Laguerre polynomial; the probability distribution of the nonlinear quantum bit in the ground state is The relationship between ,in is the probability distribution of the nonlinear quantum bit in the ground state; the classical Fisher information of the photon number parity distribution of the quantum state after translation is , the displacement accuracy is .

Images