Experimental Realization of Schumacher's Information Geometric Bell Inequality

• Published in: arXiv.org 2021-06
• Main Authors: Rezaei, Tahereh, Aslmarand, Shahabeddin M, Snyder, Robert, Khajavi, Behzad, Alsing, Paul M, Fanto, Michael, Doyeol, Ahn, Miller, Warner A
• Format: Article
• Language: English
• Subjects: BBO crystals; Bell's inequality; Correlation; Entangled states; Quantum computing; Quantum mechanics; Triangles; Visibility
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2106.00194

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.