A functorial characterization of von Neumann entropy
Quantum Physics
2022-03-22 v3 Information Theory
Category Theory
math.IT
Operator Algebras
Abstract
Using convex Grothendieck fibrations, we characterize the von Neumann entropy as a functor from finite-dimensional non-commutative probability spaces and state-preserving *-homomorphisms to real numbers. Our axioms reproduce those of Baez, Fritz, and Leinster characterizing the Shannon entropy difference. The existence of disintegrations for classical probability spaces plays a crucial role in our characterization.
Keywords
Cite
@article{arxiv.2009.07125,
title = {A functorial characterization of von Neumann entropy},
author = {Arthur J. Parzygnat},
journal= {arXiv preprint arXiv:2009.07125},
year = {2022}
}
Comments
30 pages; slightly reorganized and more concise