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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: |
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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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| [1] | Bell J S 1966 Rev. Mod. Phys. 38 447 |
| [2] | Clauser J F, Horne M A, Shimony A, and Holt R A 1969 Phys. Rev. Lett. 23 880 |
| [3] | Wehner S 2006 Phys. Rev. A 73 022110 |
| [4] | Henaut L, Catani L, Browne D E, Mansfield S, and Pappa A 2018 Phys. Rev. A 98 060302 |
| [5] | Tian Z Y, Zhao Y Y, Wu H, Wang Z, and Luo L 2020 Sci. Chin. Inf. Sci. 63 180506 |
| [6] | Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, and Wootters W K 1996 Phys. Rev. Lett. 76 722 |
| [7] | Bennett C H, Bernstein H J, Popescu S, and Schumacher B 1996 Phys. Rev. A 53 2046 |
| [8] | Lee Y C, Hsieh M H, Flammia S T, and Lee R K 2014 Phys. Rev. Lett. 112 130404 |
| [9] | Tang J S, Wang Y T, Yu S, He D Y, Xu J S, Liu B H, Chen G, Sun Y N, Sun K, Han Y J, Li C F, and Guo G C 2016 Nat. Photonics 10 642 |
| [10] | Lu P F, Liu T, Liu Y, Rao X X, Lao Q F, Wu H, Zhu F, and Luo L 2024 New J. Phys. 26 013043 |
| [11] | Chefles A 1998 Phys. Lett. A 239 339 |
| [12] | Huang M Y and Lee R K 2022 Phys. Rev. A 105 052210 |
| [13] | Bagchi B and Barik S 2020 Mod. Phys. Lett. A 35 2050090 |
| [14] | Wang Q, Xu L, and He Z 2020 Laser Phys. 30 125203 |
| [15] | Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 |
| [16] | Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, and Xue P 2017 Nat. Phys. 13 1117 |
| [17] | Li J M, Harter A K, Liu J, de Melo L, Joglekar Y N, and Luo L 2019 Nat. Commun. 10 855 |
| [18] | Ding L Y, Shi K Y, Zhang Q X, Shen D N, Zhang X, and Zhang W 2021 Phys. Rev. Lett. 126 083604 |
| [19] | Bian J, Lu P F, Liu T, Wu H, Rao X X, Wang K X, Lao Q F, Liu Y, Zhu F, and Luo L 2023 Fundam. Res. 3 904 |
| [20] | Li T Y, Zhang Y S, and Yi W 2021 Chin. Phys. Lett. 38 030301 |
| [21] | Jin L and Song Z 2021 Chin. Phys. Lett. 38 024202 |
| [22] | Bruzewicz C D, Chiaverini J, McConnell R, and Sage J M 2019 Appl. Phys. Rev. 6 021314 |
| [23] | Lu P F, Rao X X, Liu T, Liu Y, Bian J, Zhu F, and Luo L 2024 Phys. Rev. A 109 042205 |
| [24] | Brody D C and Graefe E M 2012 Phys. Rev. Lett. 109 230405 |
| [25] | Wu C W, Zhang M C, Zhou Y L et al. 2023 arXiv:2304.06590 [quant-ph] |
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