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    "story_id": "mp-2026-10-28-017",
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    "headline": "Four Measurement Settings Are Both Necessary and Sufficient",
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    "dek": "For collective first and second moments of two qubits, structural bounds and explicit constructions certify a four-setting minimum.",
    "summary": "For collective first and second moments of two qubits, structural bounds and explicit constructions certify a four-setting minimum.",
    "body_text": "The researchers ask how many orthogonal projective settings can estimate several observables without bias for arbitrary states. For two-qubit first and second moments, four settings are proven necessary and sufficient; an optimized design comes within about 0.0341 percent of a fixed-allocation variance lower bound. Finite-depth reconstruction adds bias, so the advantage depends on sample regime.",
    "why_it_matters": "For collective first and second moments of two qubits, structural bounds and explicit constructions certify a four-setting minimum.",
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        "text": "For collective first and second moments of two qubits, structural bounds and explicit constructions certify a four-setting minimum.",
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    "tags": [
      "quantum measurement",
      "qubits",
      "observables",
      "estimation"
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  "sources": [
    {
      "source_id": "source-2026-10-28-019",
      "title": "arXiv preprint 2610.36525, original v1",
      "publisher": "arXiv",
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