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arXiv · 2609.24670

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

Zacharie Van Herstraeten·Nicolas J. Cerf·Ulysse Chabaud
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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 $α$-entropy for $0<α<2$. 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.

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Zacharie Van Herstraeten, Nicolas J. Cerf, Ulysse Chabaud. 2026-09-21. Wigner-positive quantum states can have lower entropy than the vacuum. https://arxiv.org/abs/2609.24670

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