accepted [ arXiv · video · slides ]
We generalize Stinespring to arbitrary completely positive normal maps between von Neumann algebra’s. (more)
In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.
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.
published [ journal (QIC) · prequel ]
We study the notion of information cost in the quantum world. (more)
We interpret Selinger and Valiron’s quantum lambda calculus in the category of completely positive normal subunital maps between von Neumann algebras, and prove that the interpretation is adequate with respect to operational semantics.
published [ invited chapter · arXiv ]
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. (more)
submitted [ preprint ]
In the present paper, convex dcpos are introduced as dcpos associated with a compatible convex structure. Convex dcpos are later used to adequately interpret PFPC, a probabilistic version of FPC, a functional programming language with recursive types.
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 [ invited chapter · arXiv ]
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. (more)
submitted [ preprint · arXiv ]
This paper introduces a novel type theory and logic for probabilistic reasoning. (more)
accepted (categories for the working philosopher) [ arXiv ]
We derive the category-theoretic backbone of quantum theory from a process ontology. (more)
published [ proceedings (ICALP) · preprint ]
This paper starts with an effect algebraic approach to the study of non-locality and contextuality. (more)
published [ journal (LMCS) ]
We demonstrate a probabilistic version of Gelfand duality, involving the “Radon” monad on the category of compact Hausdorff space. (more)
published [ proceedings (QPL) · preprint · slides ]
The category of effectuses is equivalent to the category of FinPACs with effects, via the Kleisli construction for the lift monad (-)+1.
published [ proceedings (QPL) · preprint ]
A universal property for \( A \mapsto \sqrt{B} A \sqrt{B} \) appears in a chain of adjunctions.
published [ proceedings (MFPS) ]
We propose a new ‘quantum domain theory’ in which Scott-continuous functions are replaced by Scott-continuous natural transformations. (more)
published [ proceedings (MFPS) · preprint · slides ]
The step from probability measure to integral gets a universal property with the aid of ω-complete effect algebras and ω-complete effect modules.
The category of positive unital linear maps between C*-algebras is the Kleisli category of a comonad on the subcategory of unital *-homomorphisms between C*-algebras. (more)
published [ proceedings (POPL) · preprint ]
We develop a new framework of algebraic theories with linear parameters, and use it to analyze the equational reasoning principles of quantum computing and quantum programming languages. We use the framework as follows: (more)
published [ proceedings (MFPS) ]
We discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science. (more)
published [ proceedings (FoSSaCS) · preprint · 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 · DOI · slides ]
We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs — effects on the appropriate Hilbert space. (more)
published [ proceedings (QPL) · preprint · arXiv · 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 [ journal (LMCS) · arXiv ]
The basic theory of predicates as maps of the form \( X \rightarrow 1+1 \) and states of the form \( 1 \rightarrow X \), together with the duality between states and effects. This paper introduces a categorical description of instruments, which capture the side-effects associated with predicates (in the quantum case).
published [ journal (NGC) · preprint · EPTCS · slides ]
A denotational semantics for Selinger’s first-order functional quantum programming language is given by W*-algebras and normal completely positive subunital maps.
published [ journal (NGC) · preprint · EPTCS · data · sourcecode · video · slides ]
A Kochen-Specker system has at least 22 vertices. (more)
done supervised by Bart Jacobs [ pdf ]
An investigation of the sequential product on predicates in the framework of Jacobs.
published [ proceedings (LICS) · preprint ]
Continuous probabilistic computation is shown to fit in the effect-theoretic framework. (more)