  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.
