Experimental Realization of Schumacher's Information Geometric Bell Inequality

• URL: http://arxiv.org/abs/2106.00194v1
• Date: Tue, 1 Jun 2021 02:45:47 GMT
• Title: Experimental Realization of Schumacher's Information Geometric Bell Inequality
• Authors: Tahereh Rezaei and Shahabeddin M. Aslmarand and Robert Snyder and Behzad Khajavi and Paul M. Alsing and Michael Fanto and Doyeol (David) Ahn and Warner A. Miller
• Abstract summary: Quantum mechanics can produce correlations that are stronger than classically allowed. In 1991 Schumacher forwarded a beautiful geometric approach, analogous to the well-known result of Bell. Here we experimentally-reproduce his construction and demonstrate a definitive violation for a Bell state of two photons.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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