Details
| Original language | English |
|---|---|
| Article number | 435306 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 57 |
| Issue number | 43 |
| Publication status | Published - 11 Oct 2024 |
Abstract
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position and momentum or spin observables. This allows us to introduce symmetries which transform the outcomes of the observables used to construct the Wigner representation; we obtain several results for when these symmetries are well defined or when they uniquely specify the Wigner representation.
Keywords
- foundations of quantum theory, general probabilistic theories, Wigner representations
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Journal of Physics A: Mathematical and Theoretical, Vol. 57, No. 43, 435306, 11.10.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Symmetries and Wigner representations of operational theories
AU - Ohst, Ties A.
AU - Plávala, Martin
N1 - Publisher Copyright: © 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
PY - 2024/10/11
Y1 - 2024/10/11
N2 - We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position and momentum or spin observables. This allows us to introduce symmetries which transform the outcomes of the observables used to construct the Wigner representation; we obtain several results for when these symmetries are well defined or when they uniquely specify the Wigner representation.
AB - We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position and momentum or spin observables. This allows us to introduce symmetries which transform the outcomes of the observables used to construct the Wigner representation; we obtain several results for when these symmetries are well defined or when they uniquely specify the Wigner representation.
KW - foundations of quantum theory
KW - general probabilistic theories
KW - Wigner representations
UR - http://www.scopus.com/inward/record.url?scp=85207714111&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2306.11519
DO - 10.48550/arXiv.2306.11519
M3 - Article
AN - SCOPUS:85207714111
VL - 57
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 43
M1 - 435306
ER -