Experimental Demonstration of Enhanced Violations of Leggett-Garg Inequalities in a PT -Symmetric Trapped-Ion Qubit

The Leggett-Garg inequality (LGI) delineates a boundary between quantum and classical systems. While the temporal quantum correlations represented by LGIs have been extensively investigated in the Hermitian domain, the exploration of LGIs under non-Hermitian conditions remains scarce. Theoretical conjectures posit that nonunitary dynamics could transcend the boundary of LGIs set by Hermitian quantum mechanics, yet its empirical validation is lacking. Here, we demonstrate the enhanced violation of LGIs in a non-Hermitian system of a parity-time (PT)-symmetric trapped-ion qubit. The upper bounds of both the third-order parameter K3 and fourth-order parameter K4 increase with dissipation and can reach the maximum value when the system approaches the exceptional point, where K3 = C21 + C32 - C31 is comprising three two-time correlations and K4 = C21 + C32 + C43 - C41 is comprising four correlations. We also find that the lower bounds of K3 and K4 exhibit distinctive behaviors, where the lower bound of K3 remains constant, but that of K4 depends on the target states and measurement operators. These findings reveal a pronounced correlation between the dissipative nature of a quantum system and its temporal correlations.