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A functorial characterization of von Neumann entropy
September 15, 2020 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Arthur J. Parzygnat
arXiv ID
2009.07125
Category
quant-ph: Quantum Computing
Cross-listed
cs.IT,
math.CT,
math.OA
Citations
16
Venue
arXiv.org
Last Checked
5 months ago
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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