dorsal/arxiv
View SchemaQuantum Violation: Beyond Clauser-Horne-Shimony-Holt Inequality
| Authors | Hoshang Heydari |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603050 |
| URL | https://arxiv.org/abs/quant-ph/0603050 |
| DOI | 10.1088/0305-4470/39/38/012 |
| Journal | J. Phys. A: Math. Gen. 39 (2006) 11869-11875 |
Abstract
The best upper bound for the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality was first derived by Tsirelson. For increasing number of $\pm 1$ valued observables on both sites of the correlation experiment, Tsirelson obtained the Grothendieck's constant ($\mathcal{K}_{G}\approx 1.73\pm0.06$) as a limit for the maximal violation. In this paper, we construct a generalization of the CHSH inequality with four $\pm 1$ valued observables on both sites of a correlation experiment and show that the quantum violation approaching 1.58. Moreover, we estimate the maximal quantum violation of a correlation experiment for large and equal number of $\pm 1$ valued observables on both sites. In this case, the maximal quantum violation converges to $\sqrt{3}\approx1.73$ for very large $n$, which coincides with the approximate value of Grothendieck's constant.
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"abstract": "The best upper bound for the violation of the Clauser-Horne-Shimony-Holt\n(CHSH) inequality was first derived by Tsirelson. For increasing number of $\\pm\n1$ valued observables on both sites of the correlation experiment, Tsirelson\nobtained the Grothendieck\u0027s constant ($\\mathcal{K}_{G}\\approx 1.73\\pm0.06$) as\na limit for the maximal violation. In this paper, we construct a generalization\nof the CHSH inequality with four $\\pm 1$ valued observables on both sites of a\ncorrelation experiment and show that the quantum violation approaching 1.58.\nMoreover, we estimate the maximal quantum violation of a correlation experiment\nfor large and equal number of $\\pm 1$ valued observables on both sites. In this\ncase, the maximal quantum violation converges to $\\sqrt{3}\\approx1.73$ for very\nlarge $n$, which coincides with the approximate value of Grothendieck\u0027s\nconstant.",
"arxiv_id": "quant-ph/0603050",
"authors": [
"Hoshang Heydari"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/38/012",
"journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 11869-11875",
"title": "Quantum Violation: Beyond Clauser-Horne-Shimony-Holt Inequality",
"url": "https://arxiv.org/abs/quant-ph/0603050"
},
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