18 citations · 90 across the 18 of their papers we have counts for
19 papers
From orthoposets to orthomodular posets
John Harding, Gejza Jenda, Bert Lindenhovius
We show that the category of orthomodular posets is a full coreflective subcategory of the category of strong orthoposets, those orthoposets in which any two orthogonal elements ha…
Quantum graphs of homomorphisms
Andre Kornell, Bert Lindenhovius
We introduce a category of quantum graphs, whose definition is motivated entirely from noncommutative geometry. For all quantum graphs and in $\mathsf{qGph}…
Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory
Bert Lindenhovius, Vladimir Zamdzhiev
We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable and a model of Intuitionistic Linear Logic in the sense o…
Monoidal Quantaloids
Gejza Jenča, Bert Lindenhovius
We investigate how to add a symmetric monoidal structure to quantaloids in a compatible way. In particular, dagger compact quantaloids turn out to have properties that are similar…
The Category of Operator Spaces and Complete Contractions
Bert Lindenhovius, Vladimir Zamdzhiev
We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable. This result, together with its symmetric monoidal closed…
Categories of quantum cpos
Andre Kornell, Bert Lindenhovius, Michael Mislove
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of…
Quantum Suplattices
Gejza Jenča, Bert Lindenhovius
Building on the theory of quantum posets, we introduce a non-commutative version of suplattices, i.e., complete lattices whose morphisms are supremum-preserving maps, which form a…
A characterisation of orthomodular spaces by Sasaki maps
Bert Lindenhovius, Thomas Vetterlein
Given a Hilbert space , the set of one-dimensional subspaces of becomes an orthoset when equipped with the orthogonality relation induced by the inner product…
Quantum CPOs
Andre Kornell, Bert Lindenhovius, Michael Mislove
We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over th…
Semantics for Variational Quantum Programming
Xiaodong Jia, Andre Kornell, Bert Lindenhovius +2
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is…
Commutative Monads for Probabilistic Programming Languages
Xiaodong Jia, Bert Lindenhovius, Michael Mislove +1
A long-standing open problem in the semantics of programming languages supporting probabilistic choice is to find a commutative monad for probability on the category DCPO. In this…
A category of quantum posets
Andre Kornell, Bert Lindenhovius, Michael Mislove
We investigate a category of quantum posets that generalizes the category of posets and monotone functions. Up to equivalence, its objects are hereditarily atomic von Neumann algeb…
Orthogeometries and AW*-algebras
John Harding, Bert Lindenhovius
Based on results of Harding, Heunen, Lindenhovius and Navara, (2019), we give a connection between the category of AW*-algebras and their normal Jordan homomorphisms and a category…
LNL-FPC: The Linear/Non-linear Fixpoint Calculus
Bert Lindenhovius, Michael Mislove, Vladimir Zamdzhiev
We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which e…
Symmetries in exact Bohrification
Klaas Landsman, Bert Lindenhovius
The `Bohrification" program in the foundations of quantum mechanics implements Bohr's doctrine of classical concepts through an interplay between commutative and non-commutative op…
Enriching a Linear/Non-linear Lambda Calculus: A Programming Language for String Diagrams
Bert Lindenhovius, Michael Mislove, Vladimir Zamdzhiev
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a c…
Boolean subalgebras of orthoalgebras
John Harding, Chris Heunen, Bert Lindenhovius +1
We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to character…
Domains of commutative C*-subalgebras
Chris Heunen, Bert Lindenhovius
A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dc…
Grothendieck topologies on a poset
Bert Lindenhovius
We investigate Grothendieck topologies (in the sense of sheaf theory) on a poset that are generated by some subset of . We show that such Grothendieck topologies exhaust all…