Characterizing maximally singular phase-space distributions

TL;DR

This paper characterizes the singularities of the Glauber-Sudarshan phase-space distribution in quantum optics, exploring its mathematical properties, ambiguities, and implications for identifying nonclassical light.

Contribution

It provides a rigorous distribution-theoretic analysis of the Glauber-Sudarshan distribution, including its maximal singularities, ambiguities, and the dual space for nonclassicality testing.

Findings

Maximal degree of singularities identified

Ambiguity in distribution representation demonstrated

Methods for regularizing the distribution discussed

Abstract

Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples.