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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8 Scopus citations


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 Vad=0.970. We discuss generalizations to higher dimensional multipartite quantum states.

Original languageEnglish
Article number127444
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
StatePublished - 30 Jul 2021


  • Quantum entanglement
  • Quantum mechanics


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