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Quantum Entropy Information Measures
Quantum Simulation
Entanglement Theory Quantum Correlations
Open Quantum Systems Decoherence
A functorial characterization of von Neumann entropy
arXiv
Authors: Arthur J. Parzygnat
Year
2020
Paper ID
20685
Status
Preprint
Abstract Read
~2 min
Abstract Words
53
Citations
N/A
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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- Using convex Grothendieck fibrations, we characterize the von Neumann entropy as a functor from finite-dimensional non-commutative probability spaces and state-preserving...
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