Quantum system density matrix direct characterization method based on controlled quantum measurement process

Abstract

The invention discloses a quantum system density matrix direct characterization method based on a controlled quantum measurement process, belongs to the field of quantum information science, and can realize direct characterization of a general multi-particle continuous variable quantum system density matrix. The control quantum bit is introduced to carry out controlled quantum measurement on the quantum system, the to-be-measured density matrix element is transferred into the control quantum bit, and the controlled quantum measurement process is designed to realize transfer of any density matrix element, so that direct representation of the density matrix of the general multi-particle continuous variable quantum system is realized. The characterization method comprises the following steps that for a multi-particle continuous variable quantum system, a two-level quantum entanglement state with the same particle number is selected as a control quantum bit, the quantum system is subjected to a controlled quantum measurement process, density matrix elements to be measured of the quantum system are transferred into the entangled control quantum bit, and the density matrix elements to be measured of the quantum system are obtained by measuring the control quantum bit. And direct characterization of density matrix elements of the multi-particle system is realized.

Description

Technical Field

[0001] The present invention belongs to the field of quantum information science, and in particular relates to a method for directly characterizing the density matrix of a quantum system based on a controlled quantum measurement process. Background Art

[0002] Quantum information science is one of the most important research fields in current physics, and has great potential to breed a new round of technological revolution. Its basic idea is to encode information into quantum states, realize information processing through coherent manipulation, and use the unique coherence and entanglement of quantum systems to break through the limitations of classical physical laws in principle, and promote changes in the fields of secure communication, simulation and calculation, and precision measurement. The non-classical properties of quantum states are important resources for achieving the superiority of quantum technology. Efficient and accurate characterization of quantum systems is the key to basic theoretical research and the development of new quantum technologies. However, as the scale of quantum systems increases, the experimental complexity of information-complete quantum measurements and the computational complexity required to reconstruct the density matrix of quantum systems in traditional quantum state tomography characterization methods increase sharply. In order to solve these problems, this invention proposes a new theoretical scheme suitable for direct characterization of multi-particle high-dimensional quantum systems. The direct characterization scheme is optimized for different quantum systems and application scenarios, greatly improving the efficiency and accuracy of characterization of multi-particle high-dimensional quantum systems. Its research results will provide a feasible solution for the characterization of large-scale quantum systems and lay a foundation for theoretical research and technological development in the field of quantum science. Summary of the invention

[0003] The present invention provides a new direct characterization scheme based on a controlled quantum measurement process. The core of direct characterization of the density matrix of a multi-particle continuous variable system is to introduce a control quantum bit to perform controlled quantum measurement on the quantum system, transfer the elements of the density matrix to be measured to the control quantum bit, and reconstruct the density matrix of the subsystem to be measured by measuring the control quantum bit.

[0004] To achieve the above purpose, the present invention adopts the following technical solution, including the following steps:

[0005] (1) Prepare the multi-particle quantum system to be tested, whose density matrix is where |χ><χ′|=|x 1 x 2 ...x N > <x 1′ x 2′ ...x N′ |;

[0006] (2) Preparing the auxiliary qubit The attached qubit can obtain this superposition state by Hadamard transformation using the initial state |0>;

[0007] (3) The auxiliary quantum bit pair obtained in step (2) controls the initial state of the quantum system Continuous application of CNOT gates to prepare the maximum entangled state

[0008] (4) The k-th control quantum bit acts on the k-th particle of the quantum system to obtain the final state of the controlled quantum system: in represents a controlled quantum measurement of the joint state of the kth particle and the kth control qubit, express The Hermitian conjugation of

[0009] (5) Controlling the quantum system The observable By measuring, the density matrix elements can be A direct representation of is a combination of Pauli operators,

[0010] Furthermore, step (4) specifically includes:

[0011] remember

[0012] but

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[0014] but

[0015] but

[0016] Right now

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[0018]

[0019] Beneficial effects: Based on the standard framework of direct characterization theory, this invention creatively introduces a controlled quantum measurement process, transfers the specific density matrix elements of the quantum system to be characterized to the control quantum system, greatly reduces the complexity of the density matrix representation of the continuous variable quantum system, and makes the characterization process independent of the symmetry assumption of the quantum system, and has broad generality. This invention provides new methods and ideas for studying the coherent information of the spatial pattern of light field, high-order correlation information, and the properties of the phase space of the light field. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the direct characterization theory of multi-particle quantum systems implemented in the present invention;

[0021] Figure 2 is a light path diagram of an implementation example of the present invention; DETAILED DESCRIPTION

[0022] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments:

[0023] Implementation Example

[0024] The method for directly characterizing the photon transverse spatial quantum state density matrix based on a controlled quantum measurement process comprises the following steps:

[0025] (1) Prepare the following equipment: laser, quarter wave plate (QWP), half wave plate (HWP), lithium niobate crystal (LiNbO 3 ), yttrium vanadate crystal (TC-YVO 4 ), barium borate crystal (BBO), lens, polarization beam splitter (PBS), slit, reflector, photodetector;

[0026] (2) Photon generation: Pump light is incident on two BBO crystals (BBO-HWP-BBO), and spontaneous parametric down conversion (SPDC) occurs to generate entangled photon pairs. The photons generated in this process have two degrees of freedom: polarization and spatial mode.

[0027] (3) Spatial compensation and temporal compensation: Photons pass through lithium niobate (LiNbO 3 ) and yttrium vanadate (TC-YVO 4 ) Crystals perform spatial and temporal compensation to ensure that the phase and path of photons are effectively controlled, achieving entanglement in two degrees of freedom: polarization and transverse spatial distribution of photons;

[0028] (4) Photon polarization control: Use a half-wave plate (HWP) and a polarization beam splitter (PBS) to precisely control the polarization of photons. The HWP rotates the polarization direction of the photons, while the PBS separates photons of different polarization states into different paths;

[0029] (5) Photon spatial mode control: The lens can adjust the focusing state of the light beam so that the spatial mode of the photons meets the requirements of the experimental design. The slit is used to select a specific spatial mode, thereby controlling the projection measurement of the photons in the spatial degrees of freedom.

[0030] (6) Photon polarization state is used as a control quantum system. For different photons and their polarizations, the slit is first used to perform projection measurement in x space according to the density matrix element to be measured:

[0031] (7) Using lenses and slits to achieve projection measurement in p space Thus, the density matrix information of the two-photon spatial mode is transferred to the photon polarization state;

[0032] (8) Direct characterization of the two-photon spatial mode density matrix is ​​achieved by measuring the photon polarization information.

[0033] The optical path diagram of the above implementation example is as follows Figure 2 shown.

Claims

1. A method for directly characterizing the density matrix of a general multi-particle continuous variable quantum system, characterized in that: The following steps are involved: (1) Prepare the multi-particle quantum system to be tested; (2) preparing the auxiliary qubits; (3) Continuously applying CNOT gates to the auxiliary quantum bits obtained in step (2) to control the initial state of the quantum system to prepare the maximum entangled state; (4) Applying the k-th control quantum bit to the k-th particle of the quantum system to obtain the final state of the controlled quantum system; (5) Controlling the quantum system The observable By measuring, the density matrix elements can be direct representation of .

2. The method for directly characterizing the density matrix of a general multi-particle continuous variable quantum system according to claim 1, characterized in that: The density matrix in step (1) is where |χ><χ′|=|x1x2...x N > <x1,x2,...x N′ |.

3. The method for directly characterizing the density matrix of a general multi-particle continuous variable quantum system according to claim 1, characterized in that: The attached qubit in step (2) is The superposition state can be obtained by Hadamard transformation using the initial state |0>.

4. The method for directly characterizing the density matrix of a general multi-particle continuous variable quantum system according to claim 1, characterized in that: In step (3), the initial state of the controlled quantum system is The maximum entangled state is 5. The method for directly characterizing the density matrix of a general multi-particle continuous variable quantum system according to claim 1, characterized in that: The final state of the controlled quantum system obtained in step (4) is:

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