Experimental Realization of Schumacher's Information Geometric Bell Inequality

TL;DR

This paper experimentally demonstrates Schumacher's geometric Bell inequality violation using entangled photon pairs, confirming the non-classical correlations predicted by quantum mechanics through an information geometric approach.

Contribution

The study provides the first experimental realization of Schumacher's information geometric Bell inequality with photonic entanglement.

Findings

Successful violation of Schumacher's Bell inequality with high visibility ($V_{ad}=0.970$).

Experimental validation of the geometric approach to quantum non-locality.

Discussion of potential extensions to higher-dimensional quantum states.

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.