[
  {
    "id": "ARR-2026-68GTBBQT1T83QATJ-v1",
    "type": "article",
    "title": "A four-qubit criterion for entropy minimax duality: Minimality, sharp Renyi threshold and a W-state counterexample",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          17
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-68GTBBQT1T83QATJ",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-68GTBBQT1T83QATJ/versions/v1/",
    "note": "Research preprint; ARR-2026-68GTBBQT1T83QATJ v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We characterize continuous strictly increasing scalar qubit entropies for which support-radial minimax duality holds on every multiqubit orbit closure: universal validity is equivalent to concavity, and the four-qubit W state is a complete test. Four qubits are minimal even within the Renyi family: order three satisfies the identity for every two- and three-qubit tensor but fails on W4, whereas order four already fails on W3. The sharp universal binary Renyi range is 0<alpha<=2. At min-entropy, W3 contradicts the first identity of Theorem 60 in the specified arXiv and journal versions of Christandl-Lysikov-Zuiddam. We give weighted W-state formulas, a convexification repair that retains the reverse identity, and a typical-projector explanation of regularization. Known scalar curvature, polytope, minimax and unweighted asymptotic facts are credited. Priority remains open."
  }
]