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arXiv · 2610.08146

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

Stefano Gherardini·Paolo Solinas
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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.

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Stefano Gherardini, Paolo Solinas. 2026-10-06. Operational quasiprobability formulation of non-signaling in time for macrorealism violations. https://arxiv.org/abs/2610.08146

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