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- Kenta Cho, Bart Jacobs, Bas Westerbaan, Abraham Westerbaan
- ArXiv
- 2015

Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra structure, like in topos theory, but ‘characteristic’ functions, forming effect algebras. Such effect algebras are… (More)

- Bart Jacobs, Bas Westerbaan, Bram Westerbaan
- FoSSaCS
- 2015

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)

- Kenta Cho, Bart Jacobs, Bas Westerbaan, Bram Westerbaan
- ArXiv
- 2015

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)

- Bas Westerbaan, Bastiaan E. Westerbaan
- 2013

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)

- Sander Uijlen, Bas Westerbaan
- QPL
- 2014

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)

The following full text is a preprint version which may differ from the publisher's version. We study the sequential product GN01,GG02,GG05 , the operation p * q = √ pq √ p on the set of effects, [0, 1] A , of a von Neumann algebra A that represents sequential measurement of first p and then q. In GL08 Gudder andLatémolì ere give a list of axioms based on… (More)

- Peter Schwabe, Bas Westerbaan
- SPACE
- 2016

- Abraham Westerbaan, Bas Westerbaan
- QPL
- 2016

- Sander Uijlen, Bas Westerbaan
- New Generation Computing
- 2016

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)