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We report a method that exploits a connection between quantum contextualityand graph theory to reveal any form of quantum contextuality in high-precisionexperiments. We use this technique to identify a graph which corresponds to anextreme form of quantum contextuality unnoticed before and test it usinghigh-dimensional quantum states encoded in the linear transverse momentum ofsingle photons. Our results open the door to the experimental exploration ofquantum contextuality in all its forms, including those needed for quantumcomputation.

Experimental demonstration of the connection between quantum contextuality and graph theory