Observing local realism violations with a combination of sensitive and insensitive detectors

Several systems are exhibited in which the establishment of local realism violation is achieved even when some of the detectors employed are insensitive. The insensitive detectors are homodyne detectors whose task is to determine if the amplitude of a coherent state is a or -α. This determination can be achieved with low quantum efficiency detectors when |α| is large. The other detectors employed determine whether there is an even number or an odd number of photons in a state. These detectors are sensitive since they are required to resolve the difference of one photon. For the examples given, the local realism violation is not diminished as |α| is increased.