Experimental Observation of Quantum Correlations in Modular Variables

TL;DR

This paper experimentally demonstrates quantum entanglement in modular variables of photon pairs passing through slits, comparing variance-based and entropy-based criteria, with entropy criteria showing higher effectiveness.

Contribution

It introduces an entanglement witness based on Shannon entropy for modular variables and experimentally compares it with variance-based criteria.

Findings

Entropy-based criteria outperform variance-based criteria in detecting entanglement.

Experimental validation of entanglement in modular variables of photon pairs.

Derivation of EPR-Steering criteria using variances and entropy functions.

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. {\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.