54 citations · 324 across the 30 of their papers we have counts for
5 papers · 1 filter
Bayesian inversion and the Tomita-Takesaki modular group
Luca Giorgetti, Arthur J. Parzygnat, Alessio Ranallo +1
We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the ex…
The information loss of a stochastic map
James Fullwood, Arthur J. Parzygnat
We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the condi…
Noncommutative Differential K-theory
Byungdo Park, Arthur J. Parzygnat, Corbett Redden +1
We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression for…
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…