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

Caterina Foti1,2, Teiko Heinosaari3, Sabrina Maniscalco3, and Paola Verrucchi4,1,2

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

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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.

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[1] Guillermo García-Pérez, Dario A. Chisholm, Matteo A. C. Rossi, G. Massimo Palma, and Sabrina Maniscalco, "Decoherence without entanglement and quantum Darwinism", Physical Review Research 2 1, 012061 (2020).

[2] A. A. Andrianov, M. V. Ioffe, E. A. Izotova, and O. O. Novikov, "A perturbation algorithm for the pointers of Franke–Gorini–Kossakowski–Lindblad–Sudarshan equation", The European Physical Journal Plus 135 6, 531 (2020).

[3] Adriano M. Palmieri, Federico Bianchi, Matteo G. A. Paris, and Claudia Benedetti, "Multiclass classification of dephasing channels", Physical Review A 104 5, 052412 (2021).

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

[5] Xiao-Liang Qi and Daniel Ranard, "Emergent classicality in general multipartite states and channels", Quantum 5, 555 (2021).

[6] Nina Megier, Walter T. Strunz, and Kimmo Luoma, "Continuous quantum measurement for general Gaussian unravelings can exist", Physical Review Research 2 4, 043376 (2020).

[7] Karl Svozil, "Quantum Randomness is Chimeric", Entropy 23 5, 519 (2021).

[8] Caterina Foti, Alessandro Coppo, Giulio Barni, Alessandro Cuccoli, and Paola Verrucchi, "Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states", Nature Communications 12 1, 1787 (2021).

[9] A. De Pasquale, C. Foti, A. Cuccoli, V. Giovannetti, and P. Verrucchi, "Dynamical model for positive-operator-valued measures", Physical Review A 100 1, 012130 (2019).

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