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In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic enrichments.
Technology of data collection and information transmission is based on various mathematical models of encoding. The words Geometry of information refer to such models, whereas the words Moufang patterns refer to various sophisticated symmetries appea
In 2018, Renes [IEEE Trans. Inf. Theory, vol. 64, no. 1, pp. 577-592 (2018)] (arXiv:1701.05583) developed a general theory of channel duality for classical-input quantum-output (CQ) channels. That result showed that a number of well-known duality res
We examine the role of information geometry in the context of classical Cramer-Rao (CR) type inequalities. In particular, we focus on Eguchis theory of obtaining dualistic geometric structures from a divergence function and then applying Amari-Nagoak
A renowned information-theoretic formula by Shannon expresses the mutual information rate of a white Gaussian channel with a stationary Gaussian input as an integral of a simple function of the power spectral density of the channel input. We give in
Quantum error-correcting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states. We propose