Clauser-Horne-Shimony-Holt Bell-inequality Violability with the Full Poincar\'e-Bloch Sphere

TL;DR

This paper experimentally investigates CHSH Bell-inequality violations across the entire Poincaré-Bloch sphere, revealing basis-dependent violation patterns for Bell and non-Bell entangled photon states.

Contribution

It provides the first comprehensive experimental verification of CHSH violations with the full Poincaré-Bloch sphere, including non-Bell states and various polarization bases.

Findings

Bell states violate CHSH with identical bases regardless of ellipticity

Bell states do not violate CHSH with different bases

Certain non-Bell maximally-entangled states violate CHSH in opposite basis conditions

Abstract

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 Poincar\'e-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.