Quasi-probability representations of quantum theory with applications to quantum information science

TL;DR

This paper reviews quasi-probability representations in quantum theory, highlighting their mathematical structure, applications in quantum information, and the significance of negativity as a marker of quantum behavior.

Contribution

It unifies various quasi-probability representations through frame theory and discusses their practical relevance in quantum information science.

Findings

Negativity in quasi-probability representations indicates non-classicality.

Frame theory provides a unified framework for different representations.

Applications include quantum state characterization and quantum computing.

Abstract

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.