Testing noncontextuality inequalities that are building blocks of quantum correlations

TL;DR

This paper experimentally tests quantum maximum probabilities for complex exclusivity graphs like the heptagon and its complement, confirming quantum predictions and challenging noncontextual hidden-variable theories.

Contribution

It provides the first experimental verification of quantum maxima for the heptagon and its complement, using advanced photon encoding techniques.

Findings

Quantum maxima for heptagon and its complement are experimentally confirmed.

Results exclude maximally noncontextual hidden-variable theories.

Good agreement with quantum theory predictions.

Abstract

Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons, nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described classically. Interestingly, quantum theory predicts that the maximum values for any of these graphs cannot be achieved in Bell inequality scenarios. With the exception of the pentagon, this prediction remained experimentally unexplored. Here we test the quantum maxima for the heptagon and the complement of the heptagon using three- and five-dimensional quantum states, respectively. In both cases, we adopt two different encodings: linear transverse momentum and orbital angular momentum of single photons. Our results exclude maximally noncontextual hidden-variable theories and are in good agreement with the maxima predicted by quantum theory.