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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, MRqp, which requires that both the QNSIT conditions are satisfied and the quasiprobability distribution constructed from the measurement outcomes is positive. We prove that MRqp 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 MRqp and NSIT conditions coincide. MRqp 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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Cite

BibTeXRIS
BibTeX
@misc{gherardini2026operational,
  title = {{Operational quasiprobability formulation of non-signaling in time for macrorealism violations}},
  author = {Stefano Gherardini and Paolo Solinas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08146},
  eprint = {2610.08146},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08146},
}
RIS
TY  - UNPB
TI  - Operational quasiprobability formulation of non-signaling in time for macrorealism violations
AU  - Stefano Gherardini
AU  - Paolo Solinas
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08146
UR  - https://arxiv.org/abs/2610.08146
AB  - 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, MR_qp, which requires that both the QNSIT conditions are satisfied and the quasiprobability distribution constructed from the measurement outcomes is positive. We prove that MR_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 MR_qp and NSIT conditions coincide. MR_qp therefore provides a more sensitive tool for testing macrorealism and can be implemented experimentally through a quantum non-demolition measurement scheme.
ER  -