submitted [ arXiv ]
We show that any normal SEA splits as the direct sum of a complete Boolean algebra, a convex normal SEA and a so-called almost-convex normal SEA.
A non-trivial σ-effectus with normalization has as scalars either {0,1} or [0,1]. When states and predicates are separating, then it must embed into the category Boolean algebras (in the first case) and into the category of Banach order-unit spaces in the second case.
It’s known that affine and relevant monads preserve respectively drop and dup equations. We prove a converse.
We prove a Representation Theorem for -complete effect monoids. (more)
The title says it all.
We propose a definition of purity for positive linear maps between Euclidean Jordan Algebras. (more)
awarded [ arXiv ]
A mathematical study of quantum computing, concentrating on two related, but independent topics. (more)
submitted [ arXiv ]
We give a new way to bound the security of QKD using only the diagrammatic behavior of complementary observables and essential uniqueness of purification for quantum channels. (more)
We explicitly construct oracles to solve binary MQ, which is the underlying hard problem of many proposed post-quantum cryptographic schemes.
published [ arXiv · EPTCS · video · slides ]
We generalize Stinespring’s Dilation Theorem to arbitrary completely positive normal maps between von Neumann algebra’s. (more)
published [ journal (JMP) ]
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)
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.