Bell Parameter Dependence on Quantizer Resolution: Evidence from Photonic and Superconducting Systems and Implications for Einstein's Local Realism
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2026
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| _version_ | 1866901962462593024 |
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| author | Castro Rouanet, Jonathan Federico |
| author_facet | Castro Rouanet, Jonathan Federico |
| contents | <p><span><span>All Bell experiments to date share a fundamental design feature: the binarization of continuous detector signals into discrete outcomes </span><span>$\{-1, +1\}$</span></span><span><span><sup></sup></span></span><span>. </span><span><span>This paper presents a local deterministic model that demonstrates how this binarization process affects the observed Bell parameter </span><span>$S$</span></span><span><span><sup></sup></span></span><span>. We derive an exact geometric function:</span></p> <div> <div>$$S(N) = \frac{2\sqrt{2}}{\pi} \cdot 2^N \cdot \sin\left(\frac{\pi}{2^N}\right)$$</div> </div> <p><span><span>where </span><span>$S$</span><span> depends strictly on the detector's quantization resolution </span><span>$N$</span><span>, growing monotonically from </span><span>$S=1.8006$</span><span> at </span><span>$N=1$</span><span> to the Tsirelson bound </span><span>$S=2\sqrt{2}$</span><span> as </span><span>$N \to \infty$</span><span>, without postulating nonlocality at any point</span></span><span><span><sup></sup><sup></sup><sup></sup></span></span><span>. </span><span><span>This curve is of purely geometric origin — computable before any experiment</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></p> <p><span><span><span>A key result is the convergence identity, verified numerically from first principles</span></span><span><span><sup></sup></span></span><span>:</span></span></p> <div> <div>$$S_{classical}(N \to \infty) = S_{quantum}(j = 1/2) = 2\sqrt{2}$$</div> </div> <p><span><span>suggesting that </span><span>$2\sqrt{2}$</span><span> is not an exclusive frontier of quantum mechanics but a geometric limit reached by both classical and quantum systems at maximum information resolution</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></p> <p>This theoretical framework is empirically validated using:</p> <ul> <li> <p><span><strong><span>NIST 2015 Public Data:</span></strong><span> showing a </span><span>$+0.53\%$</span><span> increase in </span><span>$CH_{norm}$</span><span> by adjusting the temporal resolution window across two independent runs</span></span><span><span><sup></sup><sup></sup></span></span></p> </li> <li><span><span><span><strong><span>IBM ibm_torino Quantum Hardware (2026):</span></strong><span> showing a </span><span>$+0.84\%$</span><span> increase in </span><span>$S$</span><span> using multi-threshold superconducting detectors with </span><span>$M=2^N$</span><span> real thresholds</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></span></span></li> </ul> <p><span><span><span><span><span>These results imply that the domain of validity of Bell's theorem is the binary measurement regime</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>. </span><span><span>In the continuous regime, Einstein's question about local realism remains open as a falsifiable hypothesis with exact quantitative prediction: </span><span>$S$</span><span> must grow with </span><span>$N$</span><span> at an approximate geometric rate of </span><span>$1/4$</span><span> per additional bit, verifiable with </span><span>$\ge 330,000$</span><span> shots on high-fidelity hardware</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></span></span></span></p> <p><span><span><span><span><span><strong><span>Keywords:</span></strong><span> Bell's Theorem, Local Realism, Quantization Resolution, CHSH Inequality, NIST 2015, IBM Quantum, Fine's Theorem, Tsirelson Bound, Signal Processing</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></span></span></span></span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19382118 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Bell Parameter Dependence on Quantizer Resolution: Evidence from Photonic and Superconducting Systems and Implications for Einstein's Local Realism Castro Rouanet, Jonathan Federico (4-(m-Chlorophenylcarbamoyloxy)-2-butynyl)trimethylammonium Chloride Bell's Theorem Local Realism N-bit Resolution IBM Quantum NIST Signal Processing Einstein's Local Realism Bell's Theorem EPR Paradox <p><span><span>All Bell experiments to date share a fundamental design feature: the binarization of continuous detector signals into discrete outcomes </span><span>$\{-1, +1\}$</span></span><span><span><sup></sup></span></span><span>. </span><span><span>This paper presents a local deterministic model that demonstrates how this binarization process affects the observed Bell parameter </span><span>$S$</span></span><span><span><sup></sup></span></span><span>. We derive an exact geometric function:</span></p> <div> <div>$$S(N) = \frac{2\sqrt{2}}{\pi} \cdot 2^N \cdot \sin\left(\frac{\pi}{2^N}\right)$$</div> </div> <p><span><span>where </span><span>$S$</span><span> depends strictly on the detector's quantization resolution </span><span>$N$</span><span>, growing monotonically from </span><span>$S=1.8006$</span><span> at </span><span>$N=1$</span><span> to the Tsirelson bound </span><span>$S=2\sqrt{2}$</span><span> as </span><span>$N \to \infty$</span><span>, without postulating nonlocality at any point</span></span><span><span><sup></sup><sup></sup><sup></sup></span></span><span>. </span><span><span>This curve is of purely geometric origin — computable before any experiment</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></p> <p><span><span><span>A key result is the convergence identity, verified numerically from first principles</span></span><span><span><sup></sup></span></span><span>:</span></span></p> <div> <div>$$S_{classical}(N \to \infty) = S_{quantum}(j = 1/2) = 2\sqrt{2}$$</div> </div> <p><span><span>suggesting that </span><span>$2\sqrt{2}$</span><span> is not an exclusive frontier of quantum mechanics but a geometric limit reached by both classical and quantum systems at maximum information resolution</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></p> <p>This theoretical framework is empirically validated using:</p> <ul> <li> <p><span><strong><span>NIST 2015 Public Data:</span></strong><span> showing a </span><span>$+0.53\%$</span><span> increase in </span><span>$CH_{norm}$</span><span> by adjusting the temporal resolution window across two independent runs</span></span><span><span><sup></sup><sup></sup></span></span></p> </li> <li><span><span><span><strong><span>IBM ibm_torino Quantum Hardware (2026):</span></strong><span> showing a </span><span>$+0.84\%$</span><span> increase in </span><span>$S$</span><span> using multi-threshold superconducting detectors with </span><span>$M=2^N$</span><span> real thresholds</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></span></span></li> </ul> <p><span><span><span><span><span>These results imply that the domain of validity of Bell's theorem is the binary measurement regime</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>. </span><span><span>In the continuous regime, Einstein's question about local realism remains open as a falsifiable hypothesis with exact quantitative prediction: </span><span>$S$</span><span> must grow with </span><span>$N$</span><span> at an approximate geometric rate of </span><span>$1/4$</span><span> per additional bit, verifiable with </span><span>$\ge 330,000$</span><span> shots on high-fidelity hardware</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></span></span></span></p> <p><span><span><span><span><span><strong><span>Keywords:</span></strong><span> Bell's Theorem, Local Realism, Quantization Resolution, CHSH Inequality, NIST 2015, IBM Quantum, Fine's Theorem, Tsirelson Bound, Signal Processing</span></span><span><span><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup><sup></sup></span></span><span>.</span></span></span></span></span></p> |
| title | Bell Parameter Dependence on Quantizer Resolution: Evidence from Photonic and Superconducting Systems and Implications for Einstein's Local Realism |
| topic | (4-(m-Chlorophenylcarbamoyloxy)-2-butynyl)trimethylammonium Chloride Bell's Theorem Local Realism N-bit Resolution IBM Quantum NIST Signal Processing Einstein's Local Realism Bell's Theorem EPR Paradox |
| url | https://doi.org/10.5281/zenodo.19382118 |