发表机构
DIENS, École Normale Supérieure, PSL University, CNRS, INRIA（巴黎高等师范学院，PSL大学，法国国家科学研究中心，法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造简单解析反例，否证了Wigner熵猜想和Wigner优超猜想，证明存在Wigner正性但熵低于真空的量子态，并揭示了不确定性原理与非高斯性相互作用这一物理机制。
AI 中文摘要
Wigner熵猜想认为，纯高斯态最小化非负Wigner函数的Shannon熵，即Wigner熵。我们证明，将特定的纯Wigner负性态与另一个适当选择的量子态混合，可以恢复Wigner正性，同时保留略低于真空熵的Wigner熵——但严格低于真空熵。因此，我们通过推导简单的解析反例，否证了Wigner熵猜想以及更强的Wigner优超猜想，这些反例违反熵界的幅度不超过$10^{-3}$。这种具有亚真空Wigner熵的态可以任意接近真空，并且对于$0<\alpha<2$，还可以表现出亚真空的Wigner-Rényi $\alpha$-熵。我们识别了这类态存在的物理机制，该机制源于不确定性原理与非高斯性之间的微妙相互作用。本文的关键思想是在AI工具的帮助下开发的，基于对极端非负Wigner函数的刻画。
英文摘要
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.
Comments5+12 pages, 1 figure, 3 tables. Comments welcome
