Non-classicality from the phase-space flow analysis of the Weyl-Wigner quantum mechanics

TL;DR

This paper introduces a fluid-like framework in phase-space to analyze quantum non-classicality, using fluxes of purity and entropy in the Weyl-Wigner formalism, revealing new insights into quantum decoherence and classicality.

Contribution

It develops a novel phase-space flow analysis method to quantify non-classicality via quantum information fluxes, extending understanding of quantum decoherence and classicality.

Findings

Identifies phase-space fluxes related to purity and von Neumann entropy.

Provides a new quantifier for non-classicality based on quantum flow dynamics.

Illustrates the approach with anharmonic system dynamics.

Abstract

A fluid analog of the information flux in the phase-space associated to purity and von Neumann entropy are identified in the Weyl-Wigner formalism of quantum mechanics. Once constrained by symmetry and positiveness, the encountered continuity equations provide novel quantifiers for non-classicality (non-Liouvillian fluidity) given in terms of quantum decoherence, purity and von Neumann entropy fluxes. Through definitions in the Weyl-Wigner formalism, one can identify the quantum fluctuations that distort the classical-quantum coincidence regime, and the corresponding quantum information profile, whenever some bounded $x-p$ volume of the phase-space is specified. The dynamics of anharmonic systems is investigated in order to illustrate such a novel paradigm for describing quantumness and classicality through the flux of quantum information in the phase-space.