2019•Annals of Mathematical Sciences and ApplicationsOpen access

Geometric measures of information for quantum state characterization

Warner A. Miller, Shahabeddin M. Aslmarand, Paul M. Alsing, Verinder S. Rana

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.

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Key concepts: Mutual information, Conditional entropy, Conditional mutual information, Entropy (arrow of time), Information diagram, Joint entropy, Joint probability distribution, Information theory