Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus

Caterina Foti; Teiko Heinosaari; Sabrina Maniscalco; Paola Verrucchi

doi:10.22331/q-2019-08-26-179

Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus

Caterina Foti^1,2, Teiko Heinosaari³, Sabrina Maniscalco³, and Paola Verrucchi^4,1,2

¹Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019, Sesto Fiorentino (FI), Italy
²INFN, Sezione di Firenze, I-50019, Sesto Fiorentino (FI), Italy
³QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FIN-20014, Turku, Finland
⁴ISC-CNR, at Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019, Sesto Fiorentino (FI), Italy

Published:	2019-08-26, volume 3, page 179
Eprint:	arXiv:1810.10261v3
Doi:	https://doi.org/10.22331/q-2019-08-26-179
Citation:	Quantum 3, 179 (2019).

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Abstract

We study the dynamics of a quantum system $\Gamma$ with an environment $\Xi$ made of $N$ elementary quantum components. We aim at answering the following questions: can the evolution of $\Gamma$ be characterized by some general features when $N$ becomes very large, regardless of the specific form of its interaction with each and every component of $\Xi$? In other terms: should we expect all quantum systems with a macroscopic environment to undergo a somehow similar evolution? And if yes, of what type? In order to answer these questions we use well established results from large-$N$ quantum field theories, particularly referring to the conditions ensuring a large-$N$ quantum model to be effectively described by a classical theory. We demonstrate that the fulfillment of these conditions, when properly imported into the framework of the open quantum systems dynamics, guarantees that the evolution of $\Gamma$ is always of the same type of that expected if $\Xi$ were a measuring apparatus, no matter the details of the actual interaction. On the other hand, such details are found to determine the specific basis w.r.t. which $\Gamma$ undergoes the decoherence dictated by the dynamical description of the quantum measurement process. This result wears two hats: on the one hand it clarifies the physical origin of the formal statement that, under certain conditions, any channel from $\rho_\Gamma$ to $\rho_\Xi$ takes the form of a measure-and-prepare map, as recently shown in Ref. [1]; on the other hand, it formalizes the qualitative argument that the reason why we do not observe state superpositions is the continual measurement performed by the environment.

► BibTeX data

@article{Foti2019wheneverquantum,
  doi = {10.22331/q-2019-08-26-179},
  url = {https://doi.org/10.22331/q-2019-08-26-179},
  title = {Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus},
  author = {Foti, Caterina and Heinosaari, Teiko and Maniscalco, Sabrina and Verrucchi, Paola},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {179},
  month = aug,
  year = {2019}
}

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[1] Giovanni Spaventa and Paola Verrucchi, "Nature and Origin of Operators Entering the Master Equation of an Open Quantum System", Open Systems & Information Dynamics 29 02, 2250010 (2022).

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[3] A. Coppo, A. Cuccoli, C. Foti, and P. Verrucchi, "From a quantum theory to a classical one", Soft Computing 24 14, 10315 (2020).

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[7] Guillermo Perna and Esteban Calzetta, "Limits on quantum measurement engines", Physical Review E 109 4, 044102 (2024).

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