Wigner-positive quantum states can have lower entropy than the vacuum

Abstract:The Wigner entropy conjecture posits that pure Gaussian states minimize the Shannon entropy of non-negative Wigner functions, known as the Wigner entropy. We show that mixing a specific pure Wigner-negative state with another suitably chosen quantum state can restore Wigner positivity while retaining a Wigner entropy that is slightly - but strictly - below the vacuum entropy. As a consequence, we disprove the Wigner entropy conjecture, as well as the stronger Wigner majorization conjecture, by deriving simple analytical counterexamples with violations of the entropy bound no larger than $10^{-3}$. Such states with sub-vacuum Wigner entropy can be found arbitrarily close to the vacuum and can also exhibit sub-vacuum Wigner-Rényi $\alpha$-entropy for $0<\alpha<2$. We identify the physical mechanism behind the existence of such states, which arises from a subtle interplay between the uncertainty principle and non-Gaussianity. The key idea of this paper was developed with the help of AI tools, building on the characterization of extreme non-negative Wigner functions.

5+12 pages, 1 figure, 3 tables. Comments welcome

arXiv:2609.24670 [quant-ph]

(or arXiv:2609.24670v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.24670 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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