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Hat problem: a new strategy based on quantum stabilizer codes

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Abstract

The hat problem has been investigated in plenty of papers and has become a hot mathematical topic. In this paper, we will investigate the hat problem by employing quantum stabilizer code and classical Hamming code. On the one hand, a new strategy is proposed in this paper by utilizing higher-dimensional quantum stabilizer code, which, to the best of our knowledge, can be considered as a new approach to work around that problem for the first time. The solvability of the hat problem is no longer a matter of a hat game for each participant. However, it is simplified into a question about the information detected and corrected through the quantum network. On the other hand, we have performed a detailed feasibility analysis through a series of theorems in quantum space and established the implementation process with an example. Furthermore, our strategy can be applied to a variant of the more general hat problem and approximated to the optimal winning probability.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the Open Fund of Advanced Cryptography and System Security Key Laboratory of Sichuan Province (Grant No. SKLACSS-202101), NSFC (Grant Nos. 62176273, 61962009), the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (No.2019BDKFJJ010, 2019BDKFJJ014), the Fundamental Research Funds for Beijing Municipal Commission of Education, Beijing Urban Governance Research Base of North China University of Technology, the Natural Science Foundation of Inner Mongolia (2021MS06006), Baotou Kundulun District Science and technology plan project (YF2020013), and Inner Mongolia discipline inspection and supervision big data laboratory open project fund (IMDBD2020020).

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Authors and Affiliations

  1. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, No.10 Xitucheng Road, Haidian District, Beijing, 100876, China

    Liyun Zhao, Xiubo Chen & Yixian Yang

  2. School of Information Science and Technology, North China University of Technology, No.5 Jinyuanzhuang Road, Shijingshan District, Beijing, 100144, China

    Gang Xu

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  1. Liyun Zhao
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Correspondence to Xiubo Chen.

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Liyun Zhao, Gang Xu and Yixian Yang contributed equally to this work.

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Zhao, L., Chen, X., Xu, G. et al. Hat problem: a new strategy based on quantum stabilizer codes. Quantum Inf Process 21, 113 (2022). https://doi.org/10.1007/s11128-022-03451-7

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