Maximal CHSH violations with low efficiency photodetection and homodyne measurements

TL;DR

This paper demonstrates that maximal CHSH violations can be achieved with low-efficiency photodetection and homodyne measurements, providing a feasible pathway for loophole-free Bell tests with current technology.

Contribution

It characterizes the set of states that maximize CHSH violations with combined photodetection and homodyne measurements, and identifies low critical efficiencies achievable with existing detectors.

Findings

Maximal CHSH violation is attainable with the studied measurement scheme.

Critical detection efficiencies are as low as 0.29 for certain states.

Entangled cat states can achieve a critical efficiency of 0.32.

Abstract

We study nonlocality tests in which each party performs photodetection and homodyne measurements. The results of such measurements are dichotomized and a Clauser-Horne-Shimony-Holt (CHSH) inequality is used. We prove that in this scenario the maximal violation is attainable and fully characterize the set of maximally violating states. If we restrict our search to states composed by at most 2, 4, and 6 photons per mode, we find critical photodetection efficiencies of 0.48, 0.36, and 0.29. We also found an entangled variation of the famous cat states that has critical efficiency 0.32. These values are well within the limit of current photodetector technology, which suggests the present approach as a road for a loophole-free Bell experiment.