A method for characterizing the nonlocality of chain-type quantum networks

Abstract

This invention discloses a method for characterizing the nonlocality of chain-type quantum networks. This method can characterize the nonlocality of any chain-type quantum network. Based on existing chain-type quantum network models and their associated linear Bell inequalities, it constructs longer chain-type networks by adding two quantum sources and two quantum measurement devices at a time, resulting in new linear Bell inequalities. The nonlocality of this longer chain-type network is verified by the quantum violation of this inequality. The method of this invention overcomes the shortcomings of existing methods, such as slow verification efficiency and difficulty in quantifying and characterizing the nonlocality of complex quantum networks.

Description

Technical Field

[0001] This invention belongs to the field of cryptography, relates to quantum information, and particularly to a method for characterizing the nonlocality of chain-type quantum networks. Background Technology

[0002] In today's information age, a large amount of sensitive information is frequently exchanged through public communication facilities or computer networks, and the confidentiality and authenticity of this information are of paramount importance. Cryptography, through the long-term evolution and development of traditional secret-key and public-key encryption systems, has seen the emergence of various innovative theories and algorithms, greatly promoting the vigorous development of integrated network information. However, classical cryptographic systems struggle to achieve theoretically secure one-time pad encryption protocols, and random numbers play a crucial role in cryptography. Of the 61 cryptographic protocols described in the book *Applied Cryptography*, more than 40 require random numbers. However, due to the predictability of classical theories, absolutely secure random numbers cannot be generated, which can affect the security and execution efficiency of cryptographic protocols.

[0003] The emergence and rapid development of quantum key distribution protocols have made one-time pad encryption communication protocols possible, greatly ensuring the security of public information. Due to the unpredictability of quantum theory, it can generate absolutely secure random numbers, which are widely used in applications such as quantum key distribution and random number generators. Existing research shows that the fundamental reason why quantum theory can achieve information processing tasks that classical theory cannot, or even outperforms, classical information processing tasks, is its nonlocality. Currently, key indicators of quantum information processing tasks, such as quantum key generation efficiency and quantum random number generation efficiency, depend on the quantity of nonlocality. Therefore, verifying and characterizing the nonlocality in quantum networks is a very important part of quantum information processing.

[0004] Due to the existence of quantum nonlocality, quantum theory possesses intrinsic randomness. Classical theory cannot generate absolutely secure random numbers, making it difficult to meet the demand for highly secure random numbers in key generation. In contrast, random numbers generated by quantum theory are absolutely secure; even if an adversary knows the random generation mechanism and its conditions, they still cannot control all the random numbers. Therefore, quantum random numbers possess higher security. By characterizing nonlocality, the randomness in random numbers can be analyzed, providing support for the generation of quantum random numbers and thus enabling the acquisition of keys with higher security. Summary of the Invention

[0005] Purpose of the invention: In quantum information, existing technologies suffer from drawbacks such as slow construction efficiency of Bell inequality and difficulty in quantifying and characterizing nonlocality in complex quantum networks. This invention provides a method for characterizing nonlocality in chain-type quantum networks, thereby improving the efficiency and practicality of Bell inequality construction in chain-type networks.

[0006] Technical Solution: A method for characterizing the nonlocality of chain-type quantum networks. The method first estimates the input-output probabilities by statistically analyzing the input-output frequencies based on the input-output of an existing chain-type network model, thus obtaining a linear Bell inequality. Next, two sources and two measurement devices are added to the chain-type network, and the linear Bell inequality is substituted into the extended Bell inequality model for the chain-type quantum network, resulting in a newly constructed, longer chain-type quantum network with a Bell inequality. Finally, the nonlocality of the chain-type quantum network is verified based on the quantum violation of this inequality.

[0007] Furthermore, the method specifically includes the following calculation process:

[0008] (1) Calculate the corresponding probabilities based on the input and output statistics of the original chain network model, and calculate the expected value based on the probabilities. The expected value of the original chain network is... The following relationship is satisfied, where β is a real number:

[0009]

[0010] (2) Input x from the (N+1)th measuring device N+1 =0,1 are divided into two disjoint subsets. and Where x N+1 =0 corresponds to x N+1 =1 corresponds

[0011] (3) Add two sources and two measuring devices to the original chain network to form a longer chain network. The input of the two measuring devices is x. N+2 =0,1 and x N+3 =0,1, the output is and Where ω is the latent variable of the newly added source, and its corresponding new Bell inequality is expressed as follows:

[0012] ∑x + +∑x - ≤1

[0013] in,

[0014]

[0015] Furthermore, in the method, the original chain network model consists of N sources and N+1 measurement devices, and any two adjacent measurement devices share a common source. The process of processing the input and output of the measurement devices to obtain Bell's inequality through input-output frequency statistics of this network model is as follows:

[0016] (a) Each measuring device A i Randomly select x i Inputs are 0 and 1, and the measurement result output is... in It is a measuring device A i Received local latent variables;

[0017] (b) Based on the recorded input and output, the corresponding expression for local correlation is calculated as follows:

[0018] P(a 1 ,…,a N+1 |x 1 ,…,x N+1 )

[0019]

[0020] (c) Calculate the expected value in the chain network model with N sources and N+1 measurement devices. The calculation expression is as follows:

[0021]

[0022] Furthermore, the method verifies the nonlocality in a quantum network by quantum violation of Bell's inequality. Specifically, each measurement device selects a quantum state for projection measurement based on the input, records the input and output, calculates the degree of violation of Bell's inequality in the quantum system, and then verifies the nonlocality of the chain-like quantum network by violating Bell's inequality.

[0023] Beneficial effects: The nonlocality characterization method of chain quantum networks described in this invention constructs Bell's inequality for arbitrary chain quantum networks through an iterative method, verifies the nonlocality in quantum networks, not only improves the efficiency of Bell's inequality construction in chain networks, but also can characterize the nonlocality in any complex chain quantum network, and plays an important role in the practical application of nonlocality. Attached Figure Description

[0024] Figure 1 This is a model diagram illustrating an embodiment of the present invention. Detailed Implementation

[0025] To illustrate the technical solutions disclosed in this invention in detail, the following description is provided in conjunction with the accompanying drawings.

[0026] First, combining existing quantum information technology, the problem this invention aims to solve is that quantum information processing exhibits superiority and uniqueness not found in classical information processing by applying quantum nonlocality. However, existing technologies suffer from drawbacks such as slow Bell inequality construction efficiency and difficulty in quantifying and characterizing nonlocality in complex quantum networks. Compared with existing methods, this invention improves the efficiency and practicality of Bell inequality construction in chain-like networks.

[0027] Specifically, this invention provides a method for characterizing the nonlocality of chain-type quantum networks. It primarily utilizes an iterative method to construct Bell's inequality for any chain-type quantum network. Based on any existing chain-type network and its corresponding linear Bell's inequality, by adding two sources and two measurement devices, a new linear Bell's inequality can be constructed for this longer chain-type network. First, based on the inputs and outputs of the original chain-type network model, the input-output probabilities are calculated by statistically analyzing the input and output values. Based on these probabilities, the Bell's inequality of the original chain-type network is calculated. Then, by adding two sources and two measurement devices to the existing chain-type network, the aforementioned Bell's inequality is substituted into the expression of the extended Bell's inequality model for the chain-type quantum network, resulting in the Bell's inequality for the newly constructed, longer chain-type quantum network. Finally, the nonlocality of the chain-type quantum network is verified based on the quantum violation of this inequality.

[0028] Combination Figure 1 The following is a detailed description of the calculation and processing procedures involved in this invention.

[0029] In the original chain-like quantum network, there are N sources and N+1 measurement devices, where any two adjacent measurement devices share a common source. By inputting a sufficient number of times into this network and recording the corresponding outputs, the Bell inequality is obtained by statistically analyzing the input and output frequencies. If this Bell inequality is linear, adding two sources and two measurement devices to the original chain-like network allows for the construction of a linear Bell inequality for this longer chain-like network through input classification. The nonlocality of the chain-like quantum network is verified by quantum violations of the inequality. The specific steps are as follows:

[0030] S1. The original chain network consists of N sources and N+1 measurement devices, and any two adjacent measurement devices share a common source. The sources prepare and send quantum states, and the measurement devices perform quantum state measurements.

[0031] 11) Each measuring device A i Randomly select x i Inputs are 0 and 1, and the measurement result output is... in It is a measuring device A i Received local latent variables.

[0032] 12) Based on a sufficient number of input and output records, calculate the corresponding local correlation as follows:

[0033]

[0034] 13) Since the method described in this invention is simplified to a binary measurement scenario, the expected value in a chain network model with N sources and N+1 measurement devices can be easily obtained, and its calculation expression is as follows:

[0035]

[0036] S2. Construct new linear Bell inequalities for longer quantum networks with two sources and two measurement devices added.

[0037] 21) Calculate the corresponding probabilities based on a sufficient number of inputs and outputs, and then calculate the expected value based on the probabilities. The expected value of the original chain network is... It satisfies the following expression, where β is a real number:

[0038]

[0039] 22) Transfer multiple inputs x from the (N+1)th measuring device N+1 =0,1 divide into two disjoint subsets. and Where x N+1 =0 corresponds to x N+1 =1 corresponds

[0040] 23) Add two sources and two measuring devices to the original chain network to form a longer chain network. The input of the two measuring devices is x. N+2 =0,1 and x N+3 =0,1, the output is and Where ω is the hidden variable of the newly added source.

[0041] The corresponding Bell inequality is:

[0042] ∑x + +∑x - ≤1

[0043] in

[0044]

[0045] S3. Verifying the nonlocality in quantum networks through quantum violations of Bell's inequality is as follows:

[0046] 31) Each measuring device selects the quantum state for projection measurement based on the input, records the input and output, and calculates the degree of violation of Bell's inequality in the quantum system;

[0047] 32) The nonlocality of the chain-type quantum network is verified by violating Bell's inequality.

[0048] This invention provides a method for constructing Bell's inequality for any chain-like quantum network through iteration, and characterizes and verifies the nonlocality in the quantum network by quantum violations of Bell's inequality.

[0049] Quantum nonlocality is a characteristic that distinguishes quantum theory from classical theory. Due to the existence of quantum nonlocality, quantum theory possesses intrinsic randomness. By characterizing and verifying nonlocality, the randomness in random numbers can be analyzed. The greater the violation of Bell's inequality, the stronger the randomness in the generated random numbers. The method described in this invention provides support for the generation of quantum random numbers, thereby obtaining keys with higher security.

Claims

1. A method for characterizing non-locality of a chain-type quantum network, characterized by: The input and output of the chain type network model of the method are estimated for input and output probability by frequency statistics of the input and output, a linear Bell inequality is obtained, two sources and two measuring devices are added to the chain type network, the linear Bell inequality is substituted into the model of the chain type quantum network to expand the Bell inequality, a newly constructed Bell inequality of a longer chain type quantum network is obtained, and the non-locality of the chain type quantum network is verified according to the quantum violation of the inequality. The method specifically includes the following calculation process: (1) According to the input and output statistics of the original chain network model, the corresponding probability is calculated, and the expected value is calculated according to the probability. The expected value of the original chain network is satisfies the following relationship, where β is a real number: (2) divide the inputs x N+1 = 0,1 of the N+1th measuring device into two disjoint subsets and where x N+1 = 0 corresponds to x N+1 = 1 corresponds to (3) Adding two sources and two measurement devices to the original chain network to form a longer chain network, the inputs of the two measurement devices are x N+2 = 0,1 and x N+3 = 0,1, and the output is and where ω is the hidden variable of the newly added source, and the corresponding new Bell inequality is expressed as follows: ∑x + +∑x - ≤1 wherein 2. The method of claim 1, wherein: The original chain type network model is composed of N sources and N+1 measuring devices, and any two adjacent measuring devices share a common source.

3. The method of claim 2, wherein: In the process of obtaining the Bell inequality by frequency statistics of the input and output of the network model, the processing of the input and output of the measuring device is as follows: (a) each measuring device A i x is randomly chosen i = 0,1 as input, the measurement output is where is the local hidden variable received by measuring device A i from the source. (b) According to the recorded input and output, the expression of the corresponding local correlation is calculated as follows: (c) The expected value in the chain type network model with N sources and N+1 measuring devices is calculated, and the calculation expression is as follows:

4. The method of claim 1, wherein: The method verifies the non-locality in the quantum network by quantum violation of the Bell inequality, specifically including that each measuring device selects a quantum state according to the input and projection measurement, records the input and output, and calculates the degree of violation of the Bell inequality in the quantum system; then the non-locality of the chain type quantum network is verified by the violation of the Bell inequality.

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