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, ${\mathrm{MR}}_{\mathrm{qp}}$, which requires that both the QNSIT conditions are satisfied and the quasiprobability distribution constructed from the measurement outcomes is positive. We prove that ${\mathrm{MR}}_{\mathrm{qp}}$ 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 ${\mathrm{MR}}_{\mathrm{qp}}$ and NSIT conditions coincide. ${\mathrm{MR}}_{\mathrm{qp}}$ therefore provides a more sensitive tool for testing macrorealism and can be implemented experimentally through a quantum non-demolition measurement scheme.

arXiv comment7 pages, 1 figure. Comments and feedback are welcome