Characterizing the Generalized Einstein-Podolsky-Rosen State and Extensions

Abstract

In their seminal paper, Einstein Podolsky and Rosen (EPR) had introduced a momentum entangled state for two particles. That state, referred to as the EPR state, has been widely used in studies on entangled particles with continuous degrees of freedom. Later that state was generalized to a form that allows varying degree of entanglement, known as the generalized EPR state. In a suitable limit it reduces to the EPR state. The generalized EPR state is theoretically analyzed here and its entanglement quantified in terms of a recently introduced generalized entanglement measure. This state can also be applied to entangled photons produced from spontaneous parametric down conversion (SPDC). The present analysis is then used in quantifying the entanglement of photons produced from the SPDC process, in terms of certain experimental parameters. A comparison is also made with the Schmidt number, which is normally used as an entanglement measure in such situations. A procedure for experimentally determining the entanglement of SPDC photons has also been described. Furthermore, an additional state exhibiting non-Gaussian entanglement has been examined, and its entanglement has been quantified.