Twisted Fourier analysis and pseudo-probability distributions
Mathematical Physics
2020-05-19 v3 Functional Analysis
math.MP
Operator Algebras
Quantum Physics
Abstract
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary operations which correspond to phase-space transformations, generalizing Gaussian and Clifford operations. As examples, we find Wigner representations for fermions, hard-core bosons, and angle-number systems.
Cite
@article{arxiv.2004.13860,
title = {Twisted Fourier analysis and pseudo-probability distributions},
author = {Sang Jun Park and Cedric Beny and Hun Hee Lee},
journal= {arXiv preprint arXiv:2004.13860},
year = {2020}
}
Comments
It has been specified that we are recovering Mukunda's Wigner function for angle-number system. There have been some typo corrections