Experimental realization of Schumacher's information geometric Bell inequality

Quantum mechanics can produce correlations that are stronger than classically allowed. This stronger-than-classical correlation is the fuel for quantum computing. In 1991 Schumacher forwarded a beautiful geometric approach, analogous to the well-known result of Bell, to capture non-classicality of this correlation for a singlet state. He used a well-established information distance defined on an ensemble of identically-prepared states. He calculated that for certain detector settings used to measure the entangled state, the resulting geometry violated a triangle inequality - a violation that is not possible classically. This provided a novel information-based geometric Bell inequality in terms of a covariance distance. Here we experimentally reproduce his construction and demonstrate a definitive violation for a Bell state of two photons based on the usual spontaneous parametric down-conversion in a paired BBO crystal. The state we produced had a visibility of V-ad = 0.970. We discuss generalizations to higher dimensional multipartite quantum states. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

Quantum mechanics can produce correlations stronger than classically allowed, which is crucial for quantum computing. Researchers studied the non-classicality of singlet states using a geometric approach and experimentally verified a novel geometric Bell inequality. The results offer insights for generalizing to higher dimensional multipartite quantum states.