Properties of the Wigner distribution for n arbitrary operators

TL;DR

This paper generalizes the Wigner distribution to multiple operators, characterizing its properties, singularities, and positivity, and illustrating with basic examples.

Contribution

It introduces a novel generalization of the Wigner function for arbitrary operators, analyzing its mathematical properties and potential applications.

Findings

Supports lie within expectation value tuples

Characterizes singularities and positivity conditions

Provides basic illustrative examples

Abstract

We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the quantum mechanical distributions. Its role as a joint quasi-probability distribution is underlined by the property that its support always lies in the set of expectation value tuples of the operators. We characterize the set of singularities and positivity, and provide some basic examples.