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Center for Nonlinear Studies |
During the twentieth century, the probabilistic nature of quantum mechanics was demonstrated through an extensive list of multiple-measurement schemes. The most well-known of these are Bell's Inequalities, where entangled but spacially separated systems can yield correlations higher than possible in deterministic models. A second set of measurement schemes, referred to as Leggett-Garg Inequalities (LGI), similarly demonstrate this quantum reality through the temporal correlations of a single system. However, expanding Leggett-Garg Inequalities to open quantum systems requires that the coherences of the system be maintained. Here we develop an expansion of the Leggett-Garg parameter $K_{3}$ to open quantum systems through the framework of $mathcal{PT}$-symmetry, which predicts non-unitary but coherent evolution. We show that open systems allow $K_{3} \geq 1.5$, which marks the upper bound possible with unitary evolution. We found that $K_{3}$ approaches the algebraic bound as exceptional points are approached from the $mathcal{PT}$-symmetric regime, and that the algebraic bound is always achievable in the $mathcal{PT}$-broken regime. Our findings can be recreated through the postselection of systems governed by the Lindblad master equation, allowing verification through existing experimental platforms. Furthermore, our approach provides a framework for the expansion of multiple-measurement schemes such as other Leggett-Garg Inequalities, Bell Inequalities, or the Jarzynski Equality to non-Hermitian systems, while keeping the $\mathcal{PT}$-symmetric, $\mathcal{PT}$-broken, and trivially-broken regimes accessible.*
*In collaboration with Sourin Das Group and Kater Murch Lab Jacob is a postdoc in the group of Yogesh Joglekar (who is giving a quantum Lunch talk on Tuesday)
Host: Avadh Saxena