Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy

TL;DR

This paper establishes Quantum Central Limit Theorems for coarse-grained observables, showing how classical behavior emerges from quantum systems and analyzing the time evolution of differential entropy.

Contribution

It introduces Quantum Central Limit Theorems for expectation values of coarse-grained observables, highlighting a novel mechanism for classicality emergence without environmental decoherence.

Findings

Positive-definite probability distributions for expectation values

Classical behavior emerges in the large system limit

Time-dependent differential entropies are evaluated

Abstract

We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite distribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of infinitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probability distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.