Non-Hermitian CHSH* Game with a Single Trapped-Ion Qubit

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 ($PT$) 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$PT$symmetry, which is crucial for designing more robust and efficient quantum protocols.