Cohomology of Effect Algebras

Frank Roumen
(University of Cambridge)

We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

In Ross Duncan and Chris Heunen: Proceedings 13th International Conference on Quantum Physics and Logic (QPL 2016), Glasgow, Scotland, 6-10 June 2016, Electronic Proceedings in Theoretical Computer Science 236, pp. 174–201.
Published: 1st January 2017.

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