Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus
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|
|Citation:||Quantum 3, 179 (2019).|
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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. ; 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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