Fourth moments reveal the negativity of the Wigner function

TL;DR

This paper demonstrates that the negativity of the Wigner function, a key quantum property, can be detected through higher-order moments, specifically the fourth and eighth moments depending on symmetry.

Contribution

It establishes the necessity of using fourth and eighth moments to reliably detect Wigner function negativity in general and symmetric states.

Findings

Fourth moments are required to detect negativity in general states.

Eighth moments are needed for rotationally invariant Wigner functions.

Higher-order moments reveal quantum correlations linked to negativity.

Abstract

The presence of unique quantum correlations is the core of quantum information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using correlation functions defined for quasiprobability distributions. In particular we discuss the possibility of probing the negativity of a quasiprobability by comparing moments of the Wigner function. We show that one must take at least the fourth moments to find the negativity in general and the eighth moments for states with a rotationally invariant Wigner function.