Bell inequality tests using optical hybrid states to close the detection loophole

Hyukjoon Kwon and Hyunseok Jeong (Seoul National University)
 
 We study loophole-free Bell inequality tests using optical hybrid states and realistic detectors. 
The hybrid states have entanglement between a polarized single photon and a coherent field,
 and two types of schemes, on/off and photon number parity measurements, are employed to
 investigate the coherent field. When the detection efficiency is higher than 98.68%, parity
 measurements give the maximum Bell violation approaching CirelĄŻsonĄŻs bound. Under realistic
 detection efficiencies, on/off measurements give higher Bell violations than parity measurements.
 In order to close the detection loophole in the Bell inequality test, 67% of photodetector
 efficiency is required for both the measurement schemes. We note there is a trade-off between
 the threshold efficiency and the Bell violation degree in terms of a coherent amplitude |„á|, while
 |„á|<1.0 is sufficient to obtain the maximum Bell violation for most cases.