Quasiprobability representation of quantum coherence

TL;DR

This paper presents a unified method to construct quasiprobability representations for quantum coherence, enabling the certification of quantum phenomena and analysis of complex quantum correlations across various physical systems.

Contribution

A general technique for creating quasiprobability distributions for any form of quantum coherence, linking classical and quantum states through signed distributions.

Findings

Classical states have nonnegative probability distributions.

Quantum states exhibit signed quasiprobabilities indicating quantumness.

The framework applies to multipartite entanglement analysis.

Abstract

We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to analyze various forms of quantum coherence in different physical systems. Moreover, our framework renders it possible to uncover complex quantum correlations between systems, for example, via quasiprobability representations of multipartite entanglement.