Bas Westerbaan

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State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–Moore algebras of the distribution monad. This article studies some computationally relevant properties of convex sets. We introduce the term effectus for a base category with suitable coproducts (so that predicates, as arrows of the shape X → 1 + 1, form effect(More)
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic, but also in probabilistic and classical logic. This relation is presented by a long series of examples, some of them(More)
In categorical logic predicates on an object X are traditionally represented as subobjects. Jacobs proposes [9] an alternative in which the predicates on X are maps p : X → X + X with [id, id] ◦ p = id. If the coproduct of the category is well-behaved, the predicates form an effect algebra. So this approach is called effect logic. In the three prime(More)
At the heart of the Conway-Kochen Free Will Theorem and Kochen and Specker’s argument against non-contextual hidden variable theories is the existence of a Kochen-Specker (KS) system: a set of points on the sphere that has no {0,1}-coloring such that at most one of two orthogonal points are colored 1 and of three pairwise orthogonal points exactly one is(More)
It is well known that the C∗-algebra of an ordered pair of qubits is M2⊗M2. What about unordered pairs? We show in detail that M3⊕C is the C∗-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C∗-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number(More)