A functorial characterization of von Neumann entropy

• URL: http://arxiv.org/abs/2009.07125v3
• Date: Wed, 12 May 2021 21:56:35 GMT
• Title: A functorial characterization of von Neumann entropy
• Authors: Arthur J. Parzygnat
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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