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(Modular) Effect Algebras are Equivalent to (Frobenius) Antispecial Algebras by Pavlovic, Dusko; Seidel, Peter-Michael is a scholarly article available to read on EtoBox.

What is (Modular) Effect Algebras are Equivalent to (Frobenius) Antispecial Algebras about?

Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; and both come with their conceptual mysteries. A particularly elegant and mysterious constraint, imposed on Frobenius algebras to characterize a class of tripartite entangled states, is the antispecial law. A particularly contentious issue on the quantum logic side is the modularity law, proposed by von Neumann to mitigate the failure of distributivity of quantum logical connectives. We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements; and that the modularity law corresponds to the Frobenius condition. These correspondences lead to the equivalence announced in the title. Alignin

Author

Pavlovic, Dusko; Seidel, Peter-Michael

Published

2016

Language

EN