The Wigner distribution of n arbitrary observables

authored by
René Schwonnek, Reinhard F. Werner
Abstract

We study a generalization of the Wigner function to arbitrary tuples of Hermitian operators. We show that for any collection of Hermitian operators A1, ..., An and any quantum state, there is a unique joint distribution on Rn with the property that the marginals of all linear combinations of the Ak coincide with their quantum counterparts. In other words, we consider the inverse Radon transform of the exact quantum probability distributions of all linear combinations. We call it the Wigner distribution because for position and momentum, this property defines the standard Wigner function. We discuss the application to finite dimensional systems, establish many basic properties, and illustrate these by examples. The properties include the support, the location of singularities, positivity, the behavior under symmetry groups, and informational completeness.

Organisation(s)
Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)
Type
Article
Journal
Journal of mathematical physics
Volume
61
ISSN
0022-2488
Publication date
04.08.2020
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Statistical and Nonlinear Physics, Mathematical Physics
Electronic version(s)
https://doi.org/10.1063/1.5140632 (Access: Closed)