# 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

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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### Cited by

[1] 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).

[2] Guillermo García-Pérez, Dario A. Chisholm, Matteo A. C. Rossi, G. Massimo Palma, and Sabrina Maniscalco, "Decoherence without entanglement and Quantum Darwinism", arXiv:1907.12447.

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