Analysis of a proposal for a realistic loophole-free Bell test with atom-light entanglement

TL;DR

This paper analytically improves a proposed atom-light entanglement setup for loophole-free Bell tests, showing it can violate Bell inequalities under more realistic conditions, including low detection efficiency and atomic measurements.

Contribution

It provides an analytical analysis demonstrating the feasibility of Bell inequality violation with the proposed setup under realistic experimental conditions, including low photodetection efficiency.

Findings

Bell violation possible at arbitrarily low photodetection efficiency

Maximum CHSH violation of 2.29 with atomic and homodyne measurements

Minimum transmission of about 68% needed for Bell violation

Abstract

The violation of Bell inequalities where both detection and locality loopholes are closed is crucial for device independent assessments of quantum information. While of technological nature, the simultaneous closing of both loopholes still remains a challenge. In Nat. Commun. 4:2104(2013), a realistic setup to produce an atom-photon entangled state that could reach a loophole free Bell inequality violation within current experimental technology was proposed. Here we improve the analysis of this proposal by giving an analytical treatment that shows that the state proposed in Nat. Commun. 4:2104(2013) could in principle violate a Bell inequality for arbitrarily low photodetection efficiency. Moreover, it is also able to violate a Bell inequality considering only atomic and homodyne measurements eliminating the need to consider inefficient photocounting measurements. In this case, the maximum Clauser-Horne-Shimony-Holt (CHSH) inequality violation achievable is 2.29, and the minimum transmission required for violation is about 68%. Finally, we show that by postselecting on an atomic measurement, one can engineer superpositions of coherent states for various coherent state amplitudes.