Measurement of the degree of polarization entanglement through position interference

We produce polarization entangled states with variable degree of entanglement for twin photons. Entanglement in polarization is coupled to entanglement in position that produces transverse coincidence interference fringes. We show both theoretically and experimentally that we can use the position interference pattern to measure the polarization degree of entanglement. The coupling between polarization and transverse degrees of freedom are demonstrated to be useful in the manipulation of the entanglement of the twin photons.