Violation of an extended Wigner inequality with high-angular-momentum states

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. We thus demonstrate the versatility of this inequality under very lossy conditions.