{
  "id": "oai:papers.qnfo.org:a-deterministic-interface-model-for-quantum-statistics-born-rule-interference-an",
  "slug": "a-deterministic-interface-model-for-quantum-statistics-born-rule-interference-an",
  "title": "A Deterministic Interface Model for Quantum Statistics: Born Rule, Interference, and Measurement-Dependence Budgets for Loophole-Free Bell Correlations",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Device-independent quantum key distribution and certified random-number generation derive their security guarantees from the magnitude of Bell violations, and those guarantees are only as strong as the assumption of measurement independence between setting choices and hidden variables. No published computable alternative model tells the certification engineer how much violation a bounded amount of measurement dependence can fake. We build such a model: a continuous deterministic state space with a measure-preserving, mixing flow, observed through a finite measurement partition. From these premises we derive the Born rule as the invariant measure of a measurement basin, reproduce single- and sequential-measurement interference as p_A(φ) = (1+cosφ)/2 (giving p_A = 0.75 at φ = π/3), and rederive the CHSH bounds algebraically: the local bound S ≤ 2 and the quantum value S = 2√2 ≈ 2.82842712, an excess of 41.42\\% over the local bound. Within a binary conspiratorial split, exact reproduction of the quantum correlations requires full measurement dependence (δ = 1), while matching each correlator to precision ε requires a budget δ ≥ ε/2; a necessary budget for the Tsirelson value is δ ≥ 0.10355339. Comparing an independent mutual-information parametrization, reaching the Tsirelson value requires I_min = (√2-1)/2 ≈ 0.20710678 bit, exceeding the published 1/15 ≈ 0.06666667 bit relaxation benchmark, so a model respecting that benchmark caps at S_max = 34/15 ≈ 2.26666667. The model is analytical and unreviewed (TRL 1–2); its immediate use is as a null model for device-independent certification, and the next concrete test is a reanalysis of existing Bell data under an independently bounded measurement-dependence budget.",
  "abstract_markdown": "Device-independent quantum key distribution and certified random-number generation derive their security guarantees from the magnitude of Bell violations, and those guarantees are only as strong as the assumption of measurement independence between setting choices and hidden variables. No published computable alternative model tells the certification engineer how much violation a bounded amount of measurement dependence can fake. We build such a model: a continuous deterministic state space with a measure-preserving, mixing flow, observed through a finite measurement partition. From these premises we derive the Born rule as the invariant measure of a measurement basin, reproduce single- and sequential-measurement interference as $p_A(\\varphi) = (1+\\cos\\varphi)/2$ (giving $p_A = 0.75$ at $\\varphi = \\pi/3$), and rederive the CHSH bounds algebraically: the local bound $S \\le 2$ and the quantum value $S = 2\\sqrt{2} \\approx 2.82842712$, an excess of $41.42\\%$ over the local bound. Within a binary conspiratorial split, exact reproduction of the quantum correlations requires full measurement dependence ($\\delta = 1$), while matching each correlator to precision $\\varepsilon$ requires a budget $\\delta \\ge \\varepsilon/2$; a necessary budget for the Tsirelson value is $\\delta \\ge 0.10355339$. Comparing an independent mutual-information parametrization, reaching the Tsirelson value requires $I_{\\min} = (\\sqrt{2}-1)/2 \\approx 0.20710678$ bit, exceeding the published $1/15 \\approx 0.06666667$ bit relaxation benchmark, so a model respecting that benchmark caps at $S_{\\max} = 34/15 \\approx 2.26666667$. The model is analytical and unreviewed (TRL 1–2); its immediate use is as a null model for device-independent certification, and the next concrete test is a reanalysis of existing Bell data under an independently bounded measurement-dependence budget.",
  "date": "2026-10-16",
  "first_published": "2026-10-16",
  "last_revised": "2026-10-16T00:00:00Z",
  "modified": "2026-10-16T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/a-deterministic-interface-model-for-quantum-statistics-born-rule-interference-an",
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    "creators": [
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "A Deterministic Interface Model for Quantum Statistics: Born Rule, Interference, and Measurement-Dependence Budgets for Loophole-Free Bell Correlations"
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        "description": "Device-independent quantum key distribution and certified random-number generation derive their security guarantees from the magnitude of Bell violations, and those guarantees are only as strong as the assumption of measurement independence between setting choices and hidden variables. No published computable alternative model tells the certification engineer how much violation a bounded amount of measurement dependence can fake. We build such a model: a continuous deterministic state space with a measure-preserving, mixing flow, observed through a finite measurement partition. From these premises we derive the Born rule as the invariant measure of a measurement basin, reproduce single- and sequential-measurement interference as p_A(φ) = (1+cosφ)/2 (giving p_A = 0.75 at φ = π/3), and rederive the CHSH bounds algebraically: the local bound S ≤ 2 and the quantum value S = 2√2 ≈ 2.82842712, an excess of 41.42\\% over the local bound. Within a binary conspiratorial split, exact reproduction of the quantum correlations requires full measurement dependence (δ = 1), while matching each correlator to precision ε requires a budget δ ≥ ε/2; a necessary budget for the Tsirelson value is δ ≥ 0.10355339. Comparing an independent mutual-information parametrization, reaching the Tsirelson value requires I_min = (√2-1)/2 ≈ 0.20710678 bit, exceeding the published 1/15 ≈ 0.06666667 bit relaxation benchmark, so a model respecting that benchmark caps at S_max = 34/15 ≈ 2.26666667. The model is analytical and unreviewed (TRL 1–2); its immediate use is as a null model for device-independent certification, and the next concrete test is a reanalysis of existing Bell data under an independently bounded measurement-dependence budget.",
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