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arXiv · 2106.00194

Experimental Realization of Schumacher's Information Geometric Bell Inequality

Tahereh Rezaei·Shahabeddin M. Aslmarand·Robert Snyder·Behzad Khajavi·Paul M. Alsing·Michael Fanto·Doyeol·Ahn·Warner A. Miller
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Abstract

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 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.

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Tahereh Rezaei, Shahabeddin M. Aslmarand, Robert Snyder, Behzad Khajavi, Paul M. Alsing, Michael Fanto, Doyeol, Ahn, Warner A. Miller. 2021-06-01. Experimental Realization of Schumacher's Information Geometric Bell Inequality. https://doi.org/10.1016/j.physleta.2021.127444

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