Quasiprobability distributions for quantum-optical coherence and beyond

Abstract

We study the quasiprobability representation of quantum light, as introduced by Glauber and Sudarshan, for the unified characterization of quantum phenomena. We begin with reviewing the past and current impact of this technique. Regularization and convolution methods are specifically considered as they are accessible in experiments. We further discuss more general quantum systems for which the concept of negative probabilities can be generalized, being highly relevant for quantum information science. For analyzing quantum superpositions, we apply recently developed approaches to visualize quantum coherence of states via negative quasiprobability representations, including regularized quasiprobabilities for light and more general quantum correlated systems.

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

“…Phase-space representations of quantum mechanics such as the Wigner, P, positive-P, Q and related approaches are a powerful tool for the study and understanding of quantum mechanics [14,50,62,93,118]. Their use in recent times has been directed particularly as a tool Piotr Deuar: deuar@ifpan.edu.pl in quantum information science (see [58] and [129] for recent reviews) and for the simulation of large-scale quantum dynamics. Negativity of Wigner, P, and other phase-space quasi-distributions is a major criterion for quantumness and closely related to contextuality and nonlocality in quantum mechanics [58,65].…”

Probing nonclassicality with matrices of phase-space distributions

“…γ,N is of interest because it yields a GHZ state for |γ| → ∞ and W state for |γ| → 0, combining in an asymptotic manner two inequivalent forms of multipartite entanglement [94,14].…”

“…Consequently, a plethora of techniques to detect nonclassical properties have been developed, each coming with its own operational meanings for applications. For example, quantumness criteria which are based on correlation functions and phase-space representations have been extensively studied in the context of nonclassical light [13,14].…”

Detector-Agnostic Phase-Space Distributions

“…Because of its success, the concept of phasespace functions has been further extended to other physical scenarios; see Refs. [49,50]. To name a few, atomic ensembles [51][52][53][54] and entanglement [55][56][57] have been successfully characterized using quasiprobability distributions.…”

“…Generalized phase-space distributions are becoming increasingly important in identifying vastly different notions of quantumness; see Refs. [49,50] for thorough overviews. To date, however, such universally applicable techniques are also highly dependent on the particular response of the detectors.…”