Experimental observation of quantum correlations in modular variables

Abstract

We experimentally detect entanglement in modular position and momentum variables of photon pairs which have passed through $D$-slit apertures. We first employ an entanglement criteria recently proposed in [Phys. Rev. Lett. 106, 210501 (2011)], using variances of the modular variables. We then propose an entanglement witness for modular variables based on the Shannon entropy and test it experimentally. Finally, we derive criteria for Einstein-Podolsky-Rosen-steering correlations using variances and entropy functions. In both cases, the entropic criteria are more successful at identifying quantum correlations in our data.