Correlation between geometric phase and concurrence of variable retarders of birefringent medium

The orbital angular momentum of photon is one of the key source of quantum information. Polarized light passing through twisted special wave plates show entangled states of both spin angular momentum (SAM) and orbital angular momentum (OAM). The variable circular and linear retarders (VCR and VLR) are studied here from the view point of quantum processing of entangled states. In association with twist dependent gain of OAM, the geometric phase has been identified here both for VCR and VLR. For the application of VLR in an antenna array, we established a correlation between geometric phase and concurrence to explain the gradual flattened shape of the emergent wave by controlling the external twist of wave plates.