Warner A. Miller, Shahabeddin Mostafanazhad Aslmarand, Paul M. Alsing, Verinder S. Rana
tlooto Summary
The geometry of a joint distribution over a set of discrete random variables is analyzed and an analogous information area is defined and motivated and extended to higher-dimensional volumes.
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.
Citation format
MILLER, Warner A., et al. Geometric measures of information for quantum state characterization [preprint]. arXiv, 2019. arXiv:1905.07520.