Violation of Bell-CHSH inequality using imperfect photodetectors with optical hybrid states

TL;DR

This paper demonstrates that Bell inequality violations using optical hybrid states are robust against detection inefficiencies, enabling near-future loophole-free tests with current technology.

Contribution

It introduces a method for Bell tests with hybrid optical states that maintain violations at low detection efficiencies, approaching the Cirel'son bound.

Findings

Bell violation persists down to 67% efficiency

Parity measurements yield violations close to Cirel'son bound at >98.68% efficiency

On/off measurements produce moderate violations suitable for realistic detectors

Abstract

We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in the similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.