Objectivity of classical quantum stochastic processes

Piotr Szańkowski; Łukasz Cywiński

doi:10.22331/q-2024-06-27-1390

Objectivity of classical quantum stochastic processes

Piotr Szańkowski and Łukasz Cywiński

Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, PL 02-668 Warsaw, Poland

Published:	2024-06-27, volume 8, page 1390
Eprint:	arXiv:2304.07110v4
Doi:	https://doi.org/10.22331/q-2024-06-27-1390
Citation:	Quantum 8, 1390 (2024).

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Abstract

We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable – a prominent example of the so-called quantum stochastic process – fulfill the Kolmogorov consistency condition and thus appear to an observer as a sampling of a classical trajectory. We identify a set of physical conditions imposed on the system dynamics, that when satisfied, lead to the aforementioned trajectory interpretation of the measurement results. We then show that when another quantum system is coupled to the observable, the operator representing it can be replaced by external noise. Crucially, the realizations of this surrogate (classical) stochastic process follow the same trajectories as those measured by the observer. Therefore, it can be said that the trajectory interpretation suggested by the Kolmogorov consistent measurements also applies in contexts other than sequential measurements.

Popular summary

We investigate the conditions under which the results of sequential quantum measurements appear to the classical observer as classical trajectories. We identify several specific scenarios, such as macroscopic systems, chaotic dynamics, and particular types of decoherence, where quantum measurements align with a classical-like trajectory picture. Furthermore, we demonstrate that these classical trajectories are objective, as they are consistent across different observers and contexts, including interactions with other quantum systems.

► BibTeX data

@article{Szankowski2024objectivityof,
  doi = {10.22331/q-2024-06-27-1390},
  url = {https://doi.org/10.22331/q-2024-06-27-1390},
  title = {Objectivity of classical quantum stochastic processes},
  author = {Sza{\'{n}}kowski, Piotr and Cywi{\'{n}}ski, {\L{}}ukasz},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1390},
  month = jun,
  year = {2024}
}

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Cited by

[1] Jiaozi Wang and Philipp Strasberg, "Decoherence of Histories: Chaotic Versus Integrable Systems", Physical Review Letters 134 22, 220401 (2025).

[2] Paolo Luppi, Claudia Benedetti, and Andrea Smirne, "Temporal nonclassicality in continuous-time quantum walks", Physical Review A 113 4, 042212 (2026).

[3] Davide Lonigro, Fattah Sakuldee, Łukasz Cywiński, Dariusz Chruściński, and Piotr Szańkowski, "Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics", Quantum 8, 1447 (2024).

[4] Jiarui Zeng, Guo-Hao Xu, Weijie Huang, and Yao Yao, "Classical-quantum correspondence in noise-based dissipative systems", Physical Review A 110 6, 062219 (2024).

[5] Nataliya Arefyeva and Evgeny Polyakov, "Emergence of non-Markovian decoherent histories in an integrable environment: A tape-recorder model for local quantum observables", Physical Review A 113 6, 062225 (2026).

[6] Philipp Strasberg, Teresa E. Reinhard, and Joseph Schindler, "First Principles Numerical Demonstration of Emergent Decoherent Histories", Physical Review X 14 4, 041027 (2024).

[7] Piotr Szańkowski, "A perturbation theory for multi-time correlation functions in open quantum systems", SciPost Physics 19 3, 066 (2025).

[8] Philipp Strasberg, "Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach", SciPost Physics 15 1, 024 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 14:40:40) and SAO/NASA ADS (last updated successfully 2026-08-09 14:40:42). The list may be incomplete as not all publishers provide suitable and complete citation data.

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