Geometric measures of information for quantum state characterization

Abstract

We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information distance formula of Rokhlin and Rajski. We then define an analogous information area. We motivate this definition and discuss its properties. We extend this definition to higher-dimensional volumes. We briefly discuss the potential utility for these geometric measures in quantum information processing. arXiv:1905.07520v1 [quant-ph]

Experimental Realization of Schumacher's Information Geometric Bell Inequality

“…In first step, we generalized the information distance to area and higher dimensional volumes. This generalization is explained in detail in 13 . Second, we used these areas and volumes and examined at the geometrical properties of quantum networks.…”

“…=Here, A is information area and V is volume that are generalizations of the information length in Eq. 1 and were defined for four random variables, A, B, C and E in 13 and illustrated in Fig.…”

“…We recently proposed a generalization of Schumacher's construction from bipartite to multipartite states. In particular, we introduced a geometric-based measure of quantum reactivity that is a ratio of surface area to volume [10][11][12][13] . Schumacher's original construction for the Bell state was based on a quantum information distance measure of Rolkin and Rajski and later implemented in quantum mechanics by Zurek and Bennett et al 3,[14][15][16] .…”