DeepAI AI Chat

Conditional distributions for quantum systems

02/02/2021

∙

by Arthur J. Parzygnat, et al.

∙

∙

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 are obtained via a categorical Bayesian inversion procedure. Simple criteria establishing when such linear maps are positive are obtained. Several examples are provided, including the standard EPR scenario, where the EPR correlations are reproduced in a purely compositional (categorical) manner. A comparison between the Bayes map and the Petz recovery map is provided, illustrating some key differences.

∙ 05/01/2020

Effectus of Quantum Probability on Relational Structures

The notion of effectus from categorical logic is relevant in the emergin...

0 Octavio Zapata, et al. ∙

∙ 10/24/2022

Axioms for retrodiction: achieving time-reversal symmetry with a prior

We propose a category-theoretic definition of retrodiction and use it to...

0 Arthur J. Parzygnat, et al. ∙

∙ 09/19/2023

On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality

An extension of Cencov's categorical description of classical inference ...

0 Florio M. Ciaglia, et al. ∙

∙ 04/21/2019

Quantum channels as a categorical completion

We propose a categorical foundation for the connection between pure and ...

0 Mathieu Huot, et al. ∙

∙ 09/29/2022

Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion

We generalise an existing construction of Bayesian Lenses to admit lense...

0 Dylan Braithwaite, et al. ∙

∙ 05/11/2020

Computational Adequacy for Substructural Lambda Calculi

Substructural type systems, such as affine (and linear) type systems, ar...

0 Vladimir Zamdzhiev, et al. ∙