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arXiv:2302.14046 · International Journal of Theoretical Physics

Violation of Bell’s Inequality in the Clauser-Horne-Shimony-Holt Form with Entangled Quantum States Revisited

Carlo Cafaro, Christian Corda, Philip Cairns, А. Bingolbali

Published May 1, 2024• 4 citations
arXivHTMLPDF
DOI
10.1007/s10773-024-05627-6

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Linearly polarized projections are the tacit means for performing Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality tests using polarization-entangled photon pairs. The inequality is valid for all states on the Poincaré-Bloch sphere, but few laboratory studies have investigated violations with the full sphere. In this article, we explore the experimental verifications of the predicted violations of the CHSH inequality with Bell and non-Bell states with same and different linear and elliptically polarized basis states for each photon. We find that Bell states violate CHSH when using the same basis for both photons, regardless of their ellipticity, whereas they show no violations for photon projections in different bases. We found non-Bell maximally-entangled states for which the converse is true.
Linearly polarized projections are the tacit means for performing Clauser–Horne–Shimony–Holt (CHSH) Bell-inequality tests using polarization-entangled photon pairs. The inequality is valid for all states on the Poincaré–Bloch sphere, but few laboratory studies have investigated violations with the full sphere. In this article, we explore the experimental verifications of the predicted violations of the CHSH inequality with Bell and non-Bell states with same and different linear and elliptically polarized basis states for each photon. We find that Bell states violate CHSH when using the same basis for both photons, regardless of their ellipticity, whereas they show no violations for photon projections in different bases. We found non-Bell maximally entangled states for which the converse is true.
The Clauser-Horne-Shimony-Holt inequality (CHSH) is one of the most popular and well-studied witnesses of Bell's theorem, separating classical from quantum correlations. In this work, for every $d\ensuremath{\ge}2$, we present a generalization of the CHSH inequality with the property that maximal violation is achieved uniquely by the maximally entangled state of local dimension ddd. This provides an avenue for device-independent certification of maximally entangled states of arbitrary local dimension.