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.

Figure 1

The calculated transverse intensity pattern of a superposition of two LG modes of OAM quantum numbers 10 and $-10$ (and radial number 0), showing the 20 azimuthal intensity fringes. These fringes exist in coincidence for entangled states.

Figure 2

The setup produces two beams of entangled photons, which are then incident on slit wheels rotated to the given angles. Behind the slit wheels are bucket detectors. Fringes as a function of slit-wheel-angle difference can be seen in the coincidence counts.