Twisted Fourier analysis and pseudo-probability distributions

• URL: http://arxiv.org/abs/2004.13860v3
• Date: Sat, 16 May 2020 14:29:34 GMT
• Title: Twisted Fourier analysis and pseudo-probability distributions
• Authors: Sang Jun Park, Cedric Beny and Hun Hee Lee
• Abstract summary: We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations. We find Wigner representations for fermions, hard-core bosons, and angle-number systems.
• Score: 1.5555393702795075
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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