  In the study of systems that cannot be described classically, the Wigner
inequality, has received only a small amount of attention. In this paper we
extend the Wigner inequality - originally derived in 1969 - and show how it may
be used to contradict local realism with only coincidence detections in the
absence of two-outcome measurements - that is, for any system where only one
possible result of a pair of potential outcomes can be registered. It thus
encapsulates a much broader class of measurement schemes than could previously
violate a local-realistic inequality. This is possible due to an assumption of
"extended fairness" on the measurement outcomes, which we posit is highly
plausible. We then apply this inequality to a recently constructed setup with
access to entangled pairs of photons with very high angular momenta, in which
no previously derived local-realistic inequality could successfully be used
without making very broad assumptions. To our knowledge this experiment
constitutes a violation of local realism with the largest quanta to date. We
thus demonstrate the versatility of this inequality under very lossy
conditions.
