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Non-Hermitian CHSH$^*$ Game with a Single Trapped-Ion Qubit |
Xiao Song1†, Teng Liu1†, Ji Bian1, Pengfei Lu1, Yang Liu1,3, Feng Zhu1,2,4*, and Le Luo1,2,3,4* |
1School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China 2Shenzhen Research Institute of Sun Yat-Sen University, Shenzhen 518057, China 3Quantum Science Center of Guangdong-HongKong-Macao Greater Bay Area, Shenzhen 518048, China 4Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Zhuhai 519082, China
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Cite this article: |
Xiao Song, Teng Liu, Ji Bian et al 2024 Chin. Phys. Lett. 41 060301 |
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Abstract The Clauser–Horne–Shimony–Holt (CHSH) game provides a captivating illustration of the advantages of quantum strategies over classical ones. In a recent study, a variant of the CHSH game leveraging a single qubit system, referred to as the CHSH$^*$ game, has been identified. We demonstrate that this mapping relationship between these two games remains effective even for a non-unitary gate. Here we delve into the breach of Tsirelson's bound in a non-Hermitian system, predicting changes in the upper and lower bounds of the player's winning probability when employing quantum strategies in a single dissipative qubit system. We experimentally explore the impact of the CHSH$^*$ game on the player's winning probability in a single trapped-ion dissipative system, demonstrating a violation of Tsirelson's bound under the influence of parity-time ($\mathcal{PT}$) symmetry. These results contribute to a deeper understanding of the influence of non-Hermitian systems on quantum games and the behavior of quantum systems under $\mathcal{PT}$ symmetry, which is crucial for designing more robust and efficient quantum protocols.
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Received: 04 March 2024
Published: 03 June 2024
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