Details
| Original language | English |
|---|---|
| Article number | 082103 |
| Journal | Journal of mathematical physics |
| Volume | 61 |
| Issue number | 8 |
| Publication status | Published - 4 Aug 2020 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of mathematical physics, Vol. 61, No. 8, 082103, 04.08.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Wigner distribution of n arbitrary observables
AU - Schwonnek, René
AU - Werner, Reinhard F.
N1 - Funding information: We acknowledge support from the DFG (Grant Nos. RTG 1991 and CRC 1227 DQ-mat) and the BMBF project Q.Link.X. R.S. gratefully acknowledges A. Ketterer and A. Asadian for inspiring discussions.
PY - 2020/8/4
Y1 - 2020/8/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85094603559&partnerID=8YFLogxK
U2 - 10.1063/1.5140632
DO - 10.1063/1.5140632
M3 - Article
VL - 61
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 8
M1 - 082103
ER -