Various angle periods of parabolic coincidence fringes in violation of Bell inequality with high-dimensional two-photon entanglement

Abstract

Two quantum states of two half-charge optical vortexes with relative azimuthal angle {\pi} are orthogonal, by which two half-charge spiral phase plates with intersection angle {\pi} can be used to demonstrate a parabolic coincident fringe in the Bell inequality experiment with high-dimensional two-photon orbital angular momentum entanglement and to thereby obtain a strong Bell parameter of 3.2. I theoretically demonstrate various orthogonal relations between two quantum states, each of which is a state with a rotational symmetry superposition made up of n fractional orbital angular momentum states, where n is N. I propose a Bell inequality experiment with two n-section spiral phase plates that have these two quantum states, whereby various angle periods with parabolic coincident fringes 2{\pi}/n and Bell's parameter 3.2 in each period can be obtained.