{
  "slug": "rnyi-entropy-additivity-fails-outside-midrange-715210",
  "title": "Rényi Entropy Additivity Fails Outside Midrange",
  "dek": "Finite-dimensional projection-induced quantum channels violate minimum output p-Rényi entropy additivity for p>3/4 and 0≤p<1/4, leaving [1/4, 3/4] unresolved.",
  "summary": "Counterexamples show minimum output p-Rényi entropy additivity fails for p>3/4 and 0≤p<1/4, leaving [1/4, 3/4] open.",
  "tags": [
    "quantum-information",
    "renyi-entropy",
    "quantum-channels",
    "minimum-output-entropy",
    "additivity",
    "nonadditivity",
    "random-projections",
    "von-neumann-entropy"
  ],
  "published_at": "2026-07-18T17:03:29.494+00:00",
  "grade": 8.5,
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    "faq_questions": [
      "What does the paper prove?",
      "Which Rényi orders remain unresolved?",
      "What channels are used in the counterexamples?",
      "What is the product-conjugate Bell-state witness used for?",
      "What is the transpose-complement rank-defect witness?",
      "Does the paper improve von Neumann entropy results?",
      "Why does this matter?",
      "Why is the BibTeX field empty?"
    ],
    "entity_names": [
      {
        "name": "additivity of minimum output entropies",
        "type": "problem"
      },
      {
        "name": "minimum output p-Rényi entropy",
        "type": "quantity"
      },
      {
        "name": "Rényi order p",
        "type": "parameter"
      },
      {
        "name": "finite-dimensional projection-induced quantum channels",
        "type": "channel class"
      },
      {
        "name": "nonadditivity",
        "type": "phenomenon"
      },
      {
        "name": "product-conjugate Bell-state witness",
        "type": "proof technique"
      },
      {
        "name": "transpose-complement rank-defect witness",
        "type": "proof technique"
      },
      {
        "name": "correlated random-projection constructions",
        "type": "method"
      },
      {
        "name": "minimum output von Neumann entropy",
        "type": "quantity"
      },
      {
        "name": "output dimension threshold",
        "type": "benchmark"
      },
      {
        "name": "Belinschi, Collins and Nechida",
        "type": "prior-work authors"
      },
      {
        "name": "[1/4, 3/4]",
        "type": "interval"
      },
      {
        "name": "p>1",
        "type": "prior regime"
      },
      {
        "name": "p=1",
        "type": "prior regime"
      },
      {
        "name": "near p=0",
        "type": "prior regime"
      }
    ],
    "related_work_titles": [
      "Belinschi, Collins and Nechida on von Neumann minimum output entropy",
      "Prior nonadditivity for every Rényi order p>1",
      "Prior nonadditivity at p=1",
      "Prior near-zero Rényi entropy nonadditivity"
    ],
    "application_industries": [
      "Quantum information research",
      "Quantum computing theory",
      "Mathematical physics",
      "Academic publishing analytics"
    ],
    "glossary_terms": [
      "additivity",
      "nonadditivity",
      "minimum output p-Rényi entropy",
      "Rényi order p",
      "von Neumann point",
      "projection-induced quantum channels",
      "correlated random-projection constructions",
      "product-conjugate Bell-state witness",
      "transpose-complement rank-defect witness",
      "[1/4, 3/4]",
      "output dimension threshold"
    ]
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