Overview of the phase space formulation of quantum mechanics with application to quantum technologies

TL;DR

This paper reviews the phase-space formulation of quantum mechanics, emphasizing its applications in quantum technologies like state verification, and introduces new insights into the relations between different phase-space representations.

Contribution

It provides a comprehensive overview of phase-space methods in quantum mechanics, including novel results on the relations between various phase-space functions and their applications in quantum tech.

Findings

Enhanced understanding of phase-space functions like Wigner, Weyl, Q, and P in quantum systems

Demonstrated applications of phase-space methods in quantum state verification and device validation

New insights into the relationships between different phase-space representations

Abstract

The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase space is presented. The formulation to generate a generalized phase-space function for any arbitrary quantum system is shown, such as the Wigner and Weyl functions along with the asso ciated Q and P functions. Examples of how these different formulations have b een used in quantum technologies are provided, with a focus on discrete quantum systems, qubits in particular. Also provided are some results that, to the authors' knowledge, have not been published elsewhere. These results provide insight into the relation between different representations of phase space and how the phase-space representation is a powerful tool in understanding quantum information and quantum technologies.