Operational quasiprobability formulation of non-signaling in time for macrorealism violations

Abstract:In this paper, we introduce the concept of quasi non-signaling in time (QNSIT), which extends non-signaling in time (NSIT) to quasiprobability distributions. QNSIT requires that the marginals of the quasiprobability distribution under consideration at intermediate times remain unperturbed by the measurement back-action induced by a sequence of quantum measurements. Associated with QNSIT, we propose a quasiprobabilistic characterization of macrorealism, ${\rm MR}_{\rm qp}$, which requires that both the QNSIT conditions are satisfied and the quasiprobability distribution constructed from the measurement outcomes is positive. We prove that ${\rm MR}_{\rm qp}$ implies NSIT, whereas the converse does not hold because of hidden superposition paths generated or preserved by the system dynamics. We also prove that, for a two-level system, the ${\rm MR}_{\rm qp}$ and NSIT conditions coincide. ${\rm MR}_{\rm qp}$ therefore provides a more sensitive tool for testing macrorealism and can be implemented experimentally through a quantum non-demolition measurement scheme.

7 pages, 1 figure. Comments and feedback are welcome

arXiv:2610.08146 [quant-ph]

(or arXiv:2610.08146v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.08146 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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