s-ordered phase-space correspondences, fermions, and negativities

          @misc{ scivideos_PIRSA:24050070,
            doi = {10.48660/24050070},
            url = {https://pirsa.org/24050070},
            author = {Dangniam, Ninnat},
            keywords = {Quantum Foundations},
            language = {en},
            title = {s-ordered phase-space correspondences, fermions, and negativities},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {may},
            note = {PIRSA:24050070 see, \url{https://scivideos.org/pirsa/24050070}}
          }
          

Abstract

For continuous-variable systems, the negativities in the s-parametrized family of quasi-probability representations on a classical phase space establish a sort of hierarchy of non-classility measures. The coherent states, by design, display no negativity for any value of -1≤s≤1, meaning that sampling from the quantum probability distribution resulting from any measurement of a coherent state can be classically simulated, placing the coherent states as the most classical states according to this particular choice of phase space.

In this talk, I will describe how to construct s-ordered quasi-probability representations for finite-dimensional quantum systems when the phase space is equipped with more general group symmetries, focusing on the fermionic SO(2n) symmetry. Along the way, I will comment on an obstruction to an analogue of Hudson's theorem, namely that the only pure states that have positive s=0 Wigner functions are Gaussian states, and a possible remedy by giving up linearity in the phase-space correspondence.

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