Alternative Polarisation Geometries in Tests of Bell Inequalities

Abstract

The unitary transformation induced by an optical element on polarisation vectors corresponds to a rotation of the associated vectors in polarisation space on the Poincaré sphere. The degree of violation of a Bell inequality, which is of central interest in discriminating between hidden variable and quantum theories, involves only scalar products in polarisation space, and so is invariant under joint transformation of the relevant polarisation vectors. Conventionally, the plane of polarisation of any analyser is switched by an angle ψ of, say, π/8. The same violation is predicted if, instead, the analyser switching is performed by adding a relative phase of 2ψ through field-dependent birefringence. As with recent optical demonstrations of the Berry phase, the doubling of the angle indicates the simplicity of a unified analysis of both types of switching in polarisation space.