A functorial characterization of von Neumann entropy

Arthur J. Parzygnat

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arXiv · 2009.07125

A functorial characterization of von Neumann entropy

Arthur J. Parzygnat

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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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quant-ph cs.IT math.CT math.IT math.OA

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Arthur J. Parzygnat. 2020-09-15. A functorial characterization of von Neumann entropy. https://arxiv.org/abs/2009.07125

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