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

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 for-malizes the qualitative argument that the reason why we do not observe state superpositions is the continual measurement performed by the environment.