Quantum ghost imaging of transparent birefringent patterns with phase singularities

Quantum ghost imaging of transparent patterns is a manifestation of quantum nonlocality without classical analogy. A hyper-entangled state of photons consisting of Einstein Podolsky Rosen and polarisation entanglement is essential to obtain a quantum ghost image of a transparent birefringent pattern, which introduces a position and polarisation-dependent phase shift. The Einstein Podolsky Rosen entangled state produces the necessary position and momentum correlations of photons independent of their separation and measurement order. Whereas polarisation entanglement detects the phase shift introduced by the birefringent pattern. When a photon is passed through such a pattern, both photons share the information of the position and polarisation-dependent phase shift nonlocally. Four observables of photons are measured by detection and correlated to obtain a quantum ghost image. This paper presents experiments including a theoretical analysis on the quantum ghost imaging of transparent birefringent vortex phase-shifting patterns, where each vortex pattern has a phase singularity at its centre by its definition.