Negativity of the Coarse Grained Wigner Function as a Measure of Quantal Behavior

TL;DR

This paper investigates how coarse-graining the Wigner function can resolve issues with negativity as a measure of quantumness, ensuring proper classical limits and finite values for infinite systems.

Contribution

It introduces a coarse-graining approach to improve the negativity measure of the Wigner function, addressing its limitations in classical correspondence and infinities.

Findings

Coarse-graining makes negativity a more reliable quantumness measure.

Resolves infinite negativity issues in the infinite square well.

Ensures correct classical limit behavior.

Abstract

The negativity of a given state's Wigner function has been proposed as a measure of quantumness of that state in a unipartite system. This otherwise physically intuitive and useful phase-space measure however does not yield the right correspondence principle limit, and also turns out to yield infinite values for the infinite square well. We show that both these issues can be sensibly resolved using coarse-graining of the Wigner function.