Effect of phase and spatial distinguishability of photon pairs on the entanglement fidelity

Abstract

Polarization entanglement based cryptography uses the photon pairs generated in a spontaneous parametric down-conversion process and guarantees the security through the violation of Bell's inequality. Certain experimental parameters affects the entanglement fidelity and leads to a possible information leakage. The optical path difference of photons born at different crystals contributes to reduced fidelity, due to the extra birefringence of the nonlinear crystal. Although previous studies suggested methods to erase the distinguishability of photons by introducing compensation crystals, the phase difference, which is due to the lateral ray distribution is not studied. We used two commercially available collection optics; an aspheric and an achromatic lens. With these collection optics, the effect of collection optics on the entanglement fidelity is studied. We developed a simulation of such a system and found that aspheric collection optics is more suitable to achieve high fidelity.