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. {\bf 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.
@article{arxiv.1208.6222,
title = {Experimental Observation of Quantum Correlations in Modular Variables},
author = {M. A. D. Carvalho and J. Ferraz and G. F. Borges and P. L. de Assis and S. Pádua and S. P. Walborn},
journal= {arXiv preprint arXiv:1208.6222},
year = {2015}
}