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    "headline": "Positive Wigner Functions Fell Below the Vacuum Entropy",
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    "dek": "Explicit finite-energy states overturn a conjectured entropy floor while recovering the vacuum limit as energy vanishes.",
    "summary": "Explicit finite-energy states overturn a conjectured entropy floor while recovering the vacuum limit as energy vanishes.",
    "body_text": "The paper constructs physical quantum states whose Wigner functions remain nonnegative even though their Shannon entropy falls below the vacuum value. It supplies an explicit finite-energy counterexample and analytic finite-Fock-support families, then derives how the optimal entropy deficit closes as mean photon number approaches zero. The result is a mathematical counterexample and asymptotic analysis, not an experimental preparation report.",
    "why_it_matters": "Explicit finite-energy states overturn a conjectured entropy floor while recovering the vacuum limit as energy vanishes.",
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      "The paper constructs physical quantum states whose Wigner functions remain nonnegative even though their Shannon entropy falls below the vacuum value.",
      "The result is a mathematical counterexample and asymptotic analysis, not an experimental preparation report."
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    "tags": [
      "Wigner functions",
      "quantum entropy",
      "counterexamples"
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  "sources": [
    {
      "source_id": "source-2026-09-15-017",
      "title": "arXiv preprint 2609.13312",
      "publisher": "arXiv",
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      "published_at": "2026-09-13T20:00:00.000-04:00",
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    "title": "Positive Wigner Functions Fell Below the Vacuum Entropy",
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