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A functorial characterization of von Neumann entropy (2009.07125v3)
Published 15 Sep 2020 in quant-ph, cs.IT, math.CT, math.IT, and math.OA
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.