Bell Inequalities for Quantum Optical Fields

We show that the "practical" Bell inequalities, which use intensities as the observed variables, commonly used in quantum optics and widely accepted in the community, suffer from an inherent loophole, which severely limits the range of local hidden variable theories of light, which are invalidated by their violation. We present alternative inequalities which do not suffer from any (theoretical) loophole. The new inequalities use redefined correlation functions, which involve averaged products of local rates rather than intensities. Surprisingly, the new inequalities detect entanglement in situations in which the "practical" ones fail. Thus, we have two for the price on one: full consistency with Bell's Theorem, and better device-independent detection of entanglement.