Local sampling of the SU(1,1) Wigner function
Abstract
Despite the indisputable merits of the Wigner phase-space formulation, it has not been widely explored for systems with SU(1,1) symmetry, as a simple operational definition of the Wigner function has proved elusive in this case. We capitalize on the unique properties of the parity operator, to derive in a consistent way a \emph{bona fide} SU(1,1) Wigner function that faithfully parallels the structure of its continuous-variable counterpart. We propose an optical scheme, involving a squeezer and photon-number-resolving detectors, that allows for direct point-by-point sampling of that Wigner function. This provides an adequate framework to represent SU(1,1) states satisfactorily.
Keywords
Cite
@article{arxiv.2301.08127,
title = {Local sampling of the SU(1,1) Wigner function},
author = {N. Fabre and A. B. Klimov and G. Leuchs and L. L. Sanchez-Soto},
journal= {arXiv preprint arXiv:2301.08127},
year = {2023}
}
Comments
12 pages, 5 figures. To appear in AVS Quantum Science, Jonathan P. Dowling Memorial Special Issue: The Second Quantum Revolution