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    "story_id": "mp-2026-09-04-005",
    "source_story_id": "tmp-story-infinite-classical-communication-quantum",
    "edition_id": "mp-2026-09-04-morning-0057",
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    "headline": "Four Quantum Levels Broke Every Finite Classical Simulation",
    "slug": "four-quantum-levels-broke-every-finite-classical-simulation",
    "dek": "The qubit case needs two classical bits and the qutrit case admits a 357-bit protocol, but dimension four marks a qualitative break.",
    "summary": "The qubit case needs two classical bits and the qutrit case admits a 357-bit protocol, but dimension four marks a qualitative break.",
    "body_text": "The paper resolves how much classical communication is needed to exactly reproduce quantum communication and Bell correlations at every fixed dimension. It constructs an explicit 357-bit simulation for qutrits, extending the known two-bit qubit result. Starting with ququarts, the authors prove that no finite amount of classical communication can exactly simulate either the communication statistics or all correlations of two entangled systems, even with unlimited shared randomness. The claim concerns exact simulation, not approximate practical protocols.",
    "why_it_matters": "The qubit case needs two classical bits and the qutrit case admits a 357-bit protocol, but dimension four marks a qualitative break.",
    "limitations": [
      "The claim concerns exact simulation, not approximate practical protocols."
    ],
    "importance": 9,
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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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        "claim_id": "claim-mp-2026-09-04-005-001",
        "text": "The qubit case needs two classical bits and the qutrit case admits a 357-bit protocol, but dimension four marks a qualitative break.",
        "source_ids": [
          "source-2026-09-04-005"
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        "qualification": "The claim concerns exact simulation, not approximate practical protocols."
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    "source_ids": [
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    "tags": [
      "quantum communication",
      "Bell nonlocality",
      "simulation"
    ],
    "image_url": null,
    "corrections": []
  },
  "sources": [
    {
      "source_id": "source-2026-09-04-005",
      "title": "arXiv preprint 2609.04182",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2609.04182",
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      "source_type": "primary_research",
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      "published_at": "2026-09-03T13:57:48.000-04:00",
      "accessed_at": "2026-09-04T08:24:03.294-04:00",
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  "corrections": [],
  "publisher": {
    "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": "Four Quantum Levels Broke Every Finite Classical Simulation",
    "publisher": "The Machine Press",
    "published_at": "2026-09-04T09:00:00.000-04:00",
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