Operational and harmonic-analytic aspects of quasi-probability distributions

TL;DR

This paper explores the geometric and operational aspects of quasi-probability distributions like Husimi and Wigner, proposing a generalized framework that clarifies their relationships and operational meanings in quantum physics.

Contribution

It introduces a new scheme for formulating generalized quasi-probability distributions directly from coherent state theory, enhancing understanding of their structure and operational significance.

Findings

Derived explicit formulas for generalized quasi-probability distributions

Clarified the operational meanings of Husimi distributions

Established mutual relations between different classes of quasi-probability distributions

Abstract

Husimi distributions and Wigner distributions are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of generalized coherent state systems and operational quantum physics, and a scheme of formulating generalized version of quasi-probability distributions. Our scheme gives concrete formulae of quasi-probability distributions in more direct way from the theory of coherent state systems and clarify their operational meanings, especially of Husimi distributions and mutual relation between Husimi distributions and other classes of quasi-probability distributions.