Non-commutative disintegrations: existence and uniqueness in finite dimensions
Quantum Physics
2023-12-18 v2 Category Theory
Operator Algebras
Probability
Abstract
Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes of 2-positive (resp. positive) unital maps form a category. We prove non-commutative disintegrations are a.e. unique whenever they exist. We provide an explicit characterization for when disintegrations exist in the setting of finite-dimensional C*-algebras, and we give formulas for the associated disintegrations.
Cite
@article{arxiv.1907.09689,
title = {Non-commutative disintegrations: existence and uniqueness in finite dimensions},
author = {Arthur J. Parzygnat and Benjamin P. Russo},
journal= {arXiv preprint arXiv:1907.09689},
year = {2023}
}
Comments
slight reorganization, 51 pages, comments welcome!