Violation of the Bell--Clauser-Horne-Shimony-Holt inequality using imperfect photodetectors with optical hybrid states

Violation of the Bell–Clauser-Horne-Shimony-Holt inequality using imperfect photodetectors with optical hybrid states

Hyukjoon Kwon and Hyunseok Jeong

Phys. Rev. A 88, 052127 – Published 25 November 2013

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 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.