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\(n\rightarrow 1\) Quantum random access codes using single 3-level systems

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Abstract

Quantum random access codes (QRACs) have attracted much attention because of their different properties from random access codes. How to explore and verify optimal QRAC strategies is an important research topic in quantum cryptography. In this paper, we focus on optimal \(n\rightarrow 1\) QRACs using single 3-level systems. Here, we present a general upper bound of maximum guess probability of \(n\rightarrow 1\) QRACs using a generalized Bloch sphere representation, and the maximum guess probability is an important indicator to verify whether it is the optimal QRAC. Furthermore, the optimal \(2\rightarrow 1\) and \(3\rightarrow 1\) QRACs are obtained through analytical methods. Finally, tight upper bounds of the maximum guess probability of \(2\rightarrow 1\) and \(3\rightarrow 1\) QRACs are acquired. These results will improve QRAC-based quantum cryptography protocols, such as quantum key distributions, quantum random number generations.

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Acknowledgements

This work is supported by National Key R&D Program of China (2020YFB1005500), NSFC (Grant Nos. 61901218, 61801126, 62002162), Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK20190407, BK20200442) and China Postdoctoral Science Foundation funded Project (Grant Nos. 2018M630557, 2018T110499).

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Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Yu-Qian Zhou, Ya-Qi Dong, Qian-Kun Yao, Zhi-Yi Zhang & Dan Li

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Yu-Qian Zhou

  3. Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu, China

    Yu-Qian Zhou

  4. School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China

    Qing-Le Wang

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  1. Yu-Qian Zhou
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  2. Ya-Qi Dong
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  3. Qian-Kun Yao
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  4. Zhi-Yi Zhang
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  5. Dan Li
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  6. Qing-Le Wang
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Correspondence to Yu-Qian Zhou.

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Zhou, YQ., Dong, YQ., Yao, QK. et al. \(n\rightarrow 1\) Quantum random access codes using single 3-level systems. Quantum Inf Process 20, 377 (2021). https://doi.org/10.1007/s11128-021-03319-2

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