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

Abstract

We study the dynamics of a quantum system Γ with an environment Ξ made of N elementary quantum components. We aim at answering the following questions: can the evolution of Γ 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 Ξ? 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 Γ is always of the same type of that expected if Ξ 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 Γ 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 ρ Γ to ρ Ξ takes the form of a measure-and-prepare map, as recently shown in Ref. [1]; on the other hand, it for-Caterina Foti: caterina.foti@unifi.it malizes the qualitative argument that the reason why we do not observe state superpositions is the continual measurement performed by the environment.

Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states

“…We know that GCS are the only quantum states that survive the quantum-to-classical crossover according to Ω j i ! Ω, as described above and thoroughly discussed in the literature [30][31][32][33][34] . This means that performing a quantum measurement upon a system whose behavior can be effectively described as if it were classical is tantamount to select one GCS Ω j i to be the ancestor of the observed classical state or, which is the same, say that the combined effect of a measurement and the classical limit is to make χ 2 (Ω) become a Dirac-δ around the point Ω on M C that identifies the observed classical state.…”

Decoherence without entanglement and quantum Darwinism

“…(S.10), we can write ρ S (t) = ρ 00 ρ 01 e −iωt cos k θ t ρ 10 e iωt cos k θ t ρ 11 , (S. 14) where cos k θ t is a shorthand notation for cos k θ t = e −λt ∞ k=0 (λt) k k! cos k θ = e −λt e λt cos θ = e −λt(1−cos θ) (S. 15) and yields the coherence factor c(t) in the main text. Hence, the state of the system at time t is ρ S (t) = ρ 00 ρ 01 e −t(iω+λ(1−cos θ)) ρ 10 e t(iω−λ(1−cos θ)) ρ 11 .…”

“…[14] for infinite-dimensional ones, where it was proven that QD is generic, i.e., it occurs independently from the specific model considered (see also Ref. [15]). Note that, while the description of decoherence focuses on the dynamics of the open system only-with the environment generally being traced out-QD promotes the role of the environment from passive to active, since it assumes that it is what we actually observe to indirectly retrieve information on the system.…”

Emergent classicality in general multipartite states and channels

“…Given that not all dynamics exhibit effective classicality, one must still ask what type of many-body dynamics allow a such an effective description, and which subsystems or degrees of freedom in particular exhibit this classicality. See [3,5,23,24] for some discussion of this nature.…”