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A functorial characterization of von Neumann entropy
- Source :
- Cah. Topol. G\'eom. Diff\'er. Cat\'eg. LXIII, 1 (2022), 89-128
- Publication Year :
- 2020
-
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.<br />Comment: 30 pages; slightly reorganized and more concise
Details
- Database :
- arXiv
- Journal :
- Cah. Topol. G\'eom. Diff\'er. Cat\'eg. LXIII, 1 (2022), 89-128
- Publication Type :
- Report
- Accession number :
- edsarx.2009.07125
- Document Type :
- Working Paper