From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality

DOI10.2168/LMCS-11(2:5)2015zbMath1391.68034arXiv1303.1115MaRDI QIDQ2941753

Robert Furber, Bart Jacobs

Publication date: 25 August 2015

Published in: Logical Methods in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.1115

zbMATH Keywords

\(C^*\)-algebraquantum computationconvexfunctorRadon measuremonadcompact Hausdorff spacecommutative \(C^*\)-algebraprobabilistic computationGelfandKleisli

Mathematics Subject Classification ID

Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) (68Q10) General theory of (C^*)-algebras (46L05) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15)

Related Items (10)

The expectation monad in quantum foundations ⋮ Frobenius structures over Hilbert \(C^*\)-modules ⋮ Duality for convex monoids ⋮ From probability monads to commutative effectuses ⋮ A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics ⋮ Non-commutative disintegrations: existence and uniqueness in finite dimensions ⋮ Unnamed Item ⋮ Effectuses from monads ⋮ A Probability Monad as the Colimit of Spaces of Finite Samples ⋮ Towards a functorial description of quantum relative entropy

This page was built for publication: From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality