Nijmegen Quantum Logic Group

accepted by Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinksi, and Fabio Zanasi [ proceedings (LICS, to appear) ]

In this work we develop a DPO rewriting formalism which is able to absorb multiple Frobenius structures, thus sensibly simplifying diagrammatic reasoning in the aforementioned applications. (more)

unpublished by Bart Jacobs [ arXiv ]

An new channel-based algorithm for Bayesian inference. (more)

published (CMCS 2018) by Bart Jacobs, Paul Levy, and Jurriaan Rot [ proceedings (CMCS) ]

A unifying corecursive algebra perspective is given for coalgebraic trace semantics. (more)

published (CMCS 2018) by Alexandre Goy and Jurriaan Rot

It is shown how infinite trace semantics of probabilistic transition systems arises through a determinisation construction, which is then used in a bisimulation-based algorithm for infinite trace equivalence. (more)

unpublished by Bart Jacobs and Fabio Zanasi [ arXiv ]

An introduction to channel-based Bayesian reasoning. (more)

unpublished by Bart Jacobs and David Sprunger [ arXiv ]

Neural netst are studied in terms of forward and backward transformations. (more)

published (TYPES 2015) by Bart Jacobs and Robin Adams [ ]

A type theory for Bayesian reasoning is introduced. (more)

published (CUP) by Aleks Kissinger and Bob Coecke [ publisher ]

The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. (more)

published by Bart Jacobs and Abraham Westerbaan [ journal (ENTCS) · arxiv ]

A systematic account of various metrics on probability distributions (states) and on predicates.

published (ESOP 2017) by Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinksi, and Fabio Zanasi [ proceedings ]

We show that confluence is decidable for an extension of DPO rewriting to graphs with interfaces. (more)

published by Aleks Kissinger and Sander Uijlen [ proceedings (LICS) · arXiv ]

We present a categorical construction for modelling both definite and indefinite causal structures within a general class of process theories that include classical probability theory and quantum theory. (more)

published by Henning Basold, Damien Pous, and Jurriaan Rot [ proceedings (CALCO 2017) ]

We use companion functors to obtain an abstract GSOS-like extension result for specifications involving the second-order companion. (more)

submitted by Mathys Rennela and Sam Staton [ arXiv ]

We describe categorical models of a circuit-based (quantum) functional programming language. (more)

published by Filippo Bonchi, Matias Lee, and Jurriaan Rot [ proceedings (FSEN 2017) ]

Wc capture equivalence of open terms as bisimilarity on certain Mealy machines. (more)

published (EXPRESS/SOS 2017) by Jurriaan Rot [ arXiv ]

We show that monotone specifications - that disallow negative premises - do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional (more)

published (Journ. Math. Psych.) by Bart Jacobs [ journal (JMP) ]

The paper demonstrates the usefulness of this effect logic in quantum cognition (more)

submitted by Kenta Cho and Bart Jacobs [ arXiv ]

Disintegration and Bayesian inversion are explained in a categorical graphical language and with examples. (more)

published (MFCS 2017) by Bart Jacobs and Fabio Zanasi [ proceedings (MFCS) · preprint ]

Crossover influence is introduced and used to formalise d-separation in Bayesian networks. (more)

published (LMCS) by Bart Jacobs [ arXiv ]

Normalisation and conditioning are reformulated as total `hyper’ operations. (more)

submitted by Bart Jacobs [ arXiv ]

A mathematically precise definition of conjugate priors is given using channels. (more)

accepted by John van de Wetering [ arXiv ]

It is shown that quantum theory can be embedded into the category of quasi-probability distributions preserving convex, compositional and monoidal structure. (more)

published by Kenta Cho and Bart Jacobs [ proceedings (CALCO TOOLS 2017) · preprint · EfProb ]

A brief overview is given of the possibilities of the EfProb library. (more)

published by Mathys Rennela and Sam Staton [ proceedings (MFPS) ]

We describe categorical models of a circuit-based (quantum) functional programming language. (more)

published by Damien Pous and Jurriaan Rot [ proceedings (FoSSaCS 2017) · preprint (HAL) ]

We prove any causal function gives rise to a valid up-to-context technique. (more)

published by Bart Jacobs [ journal (LMCS) ]

A basic construction to form state-and-effect triangles for program semantics is explained and illustrated. (more)

submitted by Aleks Kissinger, Sean Tull, and Bas Westerbaan [ proceedings (QPL) · 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)

published by Bart Jacobs [ journal (JLAMP) · preprint ]

A general theory of probabilistic monads is developed and related to commutative effectuses. (more)

published by Bartek Klin and Jurriaan Rot [ journal (LMCS) ]

We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples. (more)

published by Bart Jacobs and Fabio Zanasi [ proceedings (MFPS 2016) · preprint ]

Bayesian inference is describe in terms of state and predicate transformation. (more)

published by Bart Jacobs [ proceedings (MFPS 2016) · preprint ]

Properties of a monad are identified so that its Kleisli category is a commutative effectus. (more)

published by Bart Jacobs, Jorik Mandemaker, and Robert Furber [ journal (Information and Computation) ]

The basic theory of the expectation monad is developed. (more)

published by Bas Westerbaan and Peter Schwabe [ preprint · proceedings (SPACE) ]

We explicitly construct oracles to solve binary MQ, which is the underlying hard problem of many proposed post-quantum cryptographic schemes.

published by Bart Jacobs [ proceedings (CMCS 2016) · preprint ]

The notion of strongly affine monad is introduced and related to side-effect freeness of instruments which are associated with predicates. (more)

published by Aleks Kissinger and Sander Uijlen [ proceedings (QPL) · arXiv ]

Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to causal processes. (more)

published by Bas Westerbaan and Abraham Westerbaan [ arXiv · proceedings (QPL) · video · slides ]

We generalize Stinespring to arbitrary completely positive normal maps between von Neumann algebra’s. (more)

published by Mathys Rennela, Sam Staton, and Robert Furber [ proceedings (QPL) ]

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.

published by Bas Westerbaan and Abraham Westerbaan [ journal (JMP) ]

We study the sequential product, the operation $p * q = \sqrt{p} q \sqrt{p}$ on the set of effects of a von Neumann algebra that represents sequential measurement of first $p$ and then $q$. We give four axioms which completely determine the sequential product.

published by Mathys Rennela, Iordanis Kerenidis, Mathieu Laurière, and François Le Gall [ journal (QIC) · prequel ]

We study the notion of information cost in the quantum world. (more)

accepted by Abraham Westerbaan and Kenta Cho [ arXiv ]

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 by Bart Jacobs and Jorik Mandemaker [ 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 by Mathys Rennela [ 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 by Kenta Cho, Bart Jacobs, Bas Westerbaan, and Abraham Westerbaan [ 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 by Bob Coecke, Ross Duncan, Aleks Kissinger, and Quanlong Wang [ 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)

accepted (categories for the working philosopher) by Bob Coecke and Aleks Kissinger [ arXiv ]

We derive the category-theoretic backbone of quantum theory from a process ontology. (more)

published by Robert Furber and Bart Jacobs [ journal (EPTCS) ]

A uniform description is proposed for conditional probability which applies both the the classical and to the quantum case. (more)

published by Bart Jacobs [ 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 by Sam Staton and Sander Uijlen [ proceedings (ICALP) · preprint ]

This paper starts with an effect algebraic approach to the study of non-locality and contextuality. (more)

published by Bart Jacobs and Robert Furber [ journal (LMCS) ]

We demonstrate a probabilistic version of Gelfand duality, involving the “Radon” monad on the category of compact Hausdorff space. (more)

published by Kenta Cho [ proceedings (QPL 2015) · 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 by Kenta Cho, Bart Jacobs, Bas Westerbaan, and Abraham Westerbaan [ proceedings (QPL 2015) · preprint ]

A universal property for \( A \mapsto \sqrt{B} A \sqrt{B} \) appears in a chain of adjunctions.

published by Mathys Rennela and Sam Staton [ proceedings (MFPS) ]

We propose a new ‘quantum domain theory’ in which Scott-continuous functions are replaced by Scott-continuous natural transformations. (more)

published by Bart Jacobs and Abraham Westerbaan [ 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.

published by Abraham Westerbaan [ arXiv · proceedings (QPL) · preprint ]

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 by Sam Staton [ 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 by Mathys Rennela [ proceedings (MFPS) ]

We discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science. (more)

published by Bart Jacobs, Bas Westerbaan, and Abraham Westerbaan [ 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 by Robin Adams [ 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 by Robert Furber and Bas Westerbaan [ 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 by Kenta Cho [ journal (NGC) · preprint · proceedings (QPL 2014) · 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 by Sander Uijlen and Bas Westerbaan [ journal (NGC) · preprint · EPTCS · data · sourcecode · video · slides ]

A Kochen-Specker system has at least 22 vertices. (more)

done by Bas Westerbaan supervised by Bart Jacobs [ pdf ]

An investigation of the sequential product on predicates in the framework of Jacobs.

published by Bart Jacobs [ proceedings (LICS) · preprint ]

Continuous probabilistic computation is shown to fit in the effect-theoretic framework. (more)