2 citations · 2 across the 1 of their papers we have counts for
5 papers
Towards a functorial description of quantum relative entropy
Arthur J. Parzygnat
A Bayesian functorial characterization of the classical relative entropy (KL divergence) of finite probabilities was recently obtained by Baez and Fritz. This was then generalized…
Conditional Distributions for Quantum Systems
Arthur J. Parzygnat
Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps ar…
Inverses, disintegrations, and Bayesian inversion in quantum Markov categories
Arthur J. Parzygnat
We introduce quantum Markov categories as a structure that refines and extends a synthetic approach to probability theory and information theory so that it includes quantum probabi…
Two-dimensional algebra in lattice gauge theory
Arthur J. Parzygnat
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular…
Discrete probabilistic and algebraic dynamics: a stochastic commutative Gelfand-Naimark Theorem
Arthur J. Parzygnat
We introduce a category of stochastic maps (certain Markov kernels) on compact Hausdorff spaces, construct a stochastic analogue of the Gelfand spectrum functor, and prove a stocha…