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Simulation algorithm on the quantum BB84 protocol based on Monte Carlo method in classical computer environment

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Abstract

A simulation algorithm based on the law of large number and Monte Carlo method in the classical computer environment is presented. During the simulation of the original quantum BB84 protocol in ideal environment, the sender Alice tries to send classical bit 0 or 1 to the receiver Bob, and the eavesdropper Eve tries to get the transmission information by intercepting and resending the quantum particles. The bit error rate in the quantum BB84 protocol is also given, and the value of the bit error rate can be analyzed if Eve eavesdrops the communication. In addition, the mean square error is introduced to describe the similarity between the simulation data and the theoretical data. (The smaller the mean square error is, the more reasonable the simulation will be.) In this simulation, the value of MSE is \(6.705\times 10^{-5}\) after 5000 times simulation when Eve eavesdrops the communication with the probability of 100%. The time complexity of the simulation algorithm is O(n) in our experiment. The reason why there is always an error between the simulation data and theoretical data is analyzed, and the correctness and rationality of the simulation algorithm are also analyzed.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. U1636106, 61572053) and the China Postdoctoral Science Foundation (Grant No. 2019M650020). A demo will be available at corresponding author’s github.

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Authors and Affiliations

  1. School of Computer Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Jian Li, Leilei Li, Hengji Li & Na Wang

  2. School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiubo Chen

  3. College of Computer Science and Technology, Beijing University of Technology, Beijing, 100124, China

    Yuguang Yang

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  1. Jian Li
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  2. Leilei Li
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  6. Yuguang Yang
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Correspondence to Leilei Li.

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Li, J., Li, L., Li, H. et al. Simulation algorithm on the quantum BB84 protocol based on Monte Carlo method in classical computer environment. Quantum Inf Process 19, 335 (2020). https://doi.org/10.1007/s11128-020-02836-w

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