We generalize Stinespring’s Dilation Theorem to arbitrary completely positive normal maps between von Neumann algebra’s. (more)
submitted [ arXiv ]
We study the sequential product, the operation on the set of effects of a von Neumann algebra that represents sequential measurement of first and then . We give four axioms which completely determine the sequential product.
done [ arXiv ]
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. (more)
published [ preprint · EPTCS ]
A universal property for \( A \mapsto \sqrt{B} A \sqrt{B} \) appears in a chain of adjunctions.
published [ preprint · LNCS · slides ]
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. (more)
published [ preprint · EPTCS · video · slides ]
The star-algebra \( M_2 \otimes M_2 \) models a pair of qubits. We show in detail that \( M_3 \oplus \mathbb{C} \) models an unordered pair of qubits. Then we use the late 19th century Schur-Weyl duality, to characterize the star-algebra that models an unordered n-tuple of d-level quantum systems. (more)
published [ preprint · EPTCS · journal · data · sourcecode · video · slides ]
A Kochen-Specker system has at least 22 vertices. (more)
submitted [ preprint ]
A simplification and slight extension of Statman’s Hierarchy Theorem. (more)
done supervised by prof. Bart Jacobs [ pdf ]
An investigation of the sequential product on predicates in the framework of Jacobs.
done supervised by dr. Wim Veldman [ pdf · arXiv ]
We introduce several notions of effective undecidability and show they are equivalent to previously investigated notions of completeness and creativity.