Upper bounds on the purity of Wigner positive quantum states that verify the Wigner entropy conjecture

• URL: http://arxiv.org/abs/2601.16898v1
• Date: Fri, 23 Jan 2026 17:04:43 GMT
• Title: Upper bounds on the purity of Wigner positive quantum states that verify the Wigner entropy conjecture
• Authors: Qipeng Qian, Christos Gagatsos,
• Abstract summary: We present analytical results toward the Wigner entropy conjecture.<n>We first prove that all Wigner non-negative states with $le 4-2sqrt3$ satisfy the Wigner entropy conjecture.
• Score: 1.7188280334580195
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present analytical results toward the Wigner entropy conjecture, which posits that among all physical Wigner non-negative states the Wigner entropy is minimized by pure Gaussian states for which it attains the value $1+\lnπ$.Working under a minimal set of constraints on the Wigner function, namely, non-negativity, normalization, and the pointwise bound $πW\le 1$, we construct an explicit hierarchy of lower bounds $B_n$ on $S[W]$ by combining a truncated series lower bound for $-\ln x$ with moment identities of the Wigner function.This yields closed-form purity-based sufficient conditions ensuring $S[W]\ge 1+\lnπ$.In particular, we first prove that all Wigner non-negative states with $μ\le 4-2\sqrt3$ satisfy the Wigner entropy conjecture. We further obtain a systematic purity-only relaxation of the hierarchy, yielding the simple sufficient condition $μ\le 2/e$. On top of aforesaid results, our analysis clarifies why additional physicality constraints are necessary for purity-based approaches that aim to approach the extremal case $μ\leq1$.

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