Continuous variable polarization entanglement, experiment and analysis

We generate and characterize continuous variable polarization entanglement between two optical beams. We first produce quadrature entanglement, and by performing local operations we transform it into a polarization basis. We extend two entanglement criteria, the inseparability criteria proposed by Duan et al (2000 Phys. Rev. Lett. 84 2722) and the Einstein–Podolsky–Rosen (EPR) paradox criteria proposed by Reid and Drummond (1988 Phys. Rev. Lett. 60 2731), to Stokes operators; and use them to characterize the entanglement. Our results for the EPR paradox criteria are visualized in terms of uncertainty balls on the Poincaré sphere. We demonstrate theoretically that using two quadrature entangled pairs it is possible to entangle three orthogonal Stokes operators between a pair of beams, although with a bound √3 times more stringent than for the quadrature entanglement.