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    "story_id": "mp-2026-09-04-013",
    "source_story_id": "tmp-story-thermalization-quantum-error-correction",
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    "headline": "Thermalization Hid Information as Efficiently as an Optimal Code",
    "slug": "thermalization-hid-information-as-efficiently-as-an-optimal-code",
    "dek": "Late-time many-body states trace a rate-distance curve that reaches quantum error-correction limits at infinite and finite temperature.",
    "summary": "Late-time many-body states trace a rate-distance curve that reaches quantum error-correction limits at infinite and finite temperature.",
    "body_text": "The work treats typical late-time states as codewords and applies approximate quantum-error-correction tools to thermalizing dynamics. Numerically, the extracted relation among encoding rate, distance and thermal entropy density saturates the quantum Singleton bound at infinite temperature. At finite temperature, the authors define a Scrooge-ensemble code family and prove saturation of the entropic version, while showing how conserved energy or charge can leak classical information until differences reach thermal-fluctuation scale. These are theoretical and numerical results, not a device demonstration.",
    "why_it_matters": "Late-time many-body states trace a rate-distance curve that reaches quantum error-correction limits at infinite and finite temperature.",
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      "These are theoretical and numerical results, not a device demonstration."
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    "first_published_at": "2026-09-04T09:00:00.000-04:00",
    "modified_at": "2026-09-04T09:00:00.000-04:00",
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        "text": "Late-time many-body states trace a rate-distance curve that reaches quantum error-correction limits at infinite and finite temperature.",
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        "qualification": "These are theoretical and numerical results, not a device demonstration."
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    "tags": [
      "quantum error correction",
      "thermalization",
      "many-body physics"
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  "sources": [
    {
      "source_id": "source-2026-09-04-013",
      "title": "arXiv preprint 2609.04121",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2609.04121",
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      "source_type": "primary_research",
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      "published_at": "2026-09-03T13:23:17.000-04:00",
      "accessed_at": "2026-09-04T08:24:03.294-04:00",
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    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
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  "cite_this_report": {
    "title": "Thermalization Hid Information as Efficiently as an Optimal Code",
    "publisher": "The Machine Press",
    "published_at": "2026-09-04T09:00:00.000-04:00",
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