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arXiv · 2503.09353

Grand Unification of All Discrete Wigner Functions on $d \times d$ Phase Space

Lucky K. Antonopoulos·Dominic G. Lewis·Jack Davis·Nicholas Funai·Nicolas C. Menicucci
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Abstract

Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation obscures which features are fundamental and which are artefacts of representation. We introduce a stencil-based framework that exhausts all possible $d\times d$ discrete Wigner functions for a single $d$-dimensional quantum system (including a novel one for even $d$), subsuming known forms. We also give explicit invertible linear maps between definitions within the same $d$, enabling direct comparison of operational properties and exposing representation dependence.

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Lucky K. Antonopoulos, Dominic G. Lewis, Jack Davis, Nicholas Funai, Nicolas C. Menicucci. 2025-03-12. Grand Unification of All Discrete Wigner Functions on $d \times d$ Phase Space. https://doi.org/10.1103/s5wn-mysr

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