Chris Heunen

Categories for Quantum Theory

Free Quantum Computing

Causal coverages in ordered locales and spacetimes

One rig to control them all

String diagrams for defect-based surface code computation

Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories

Quantum circuits are just a phase

Hadamard-Π: Equational quantum programming

Hilbert *-categories: where limits in analysis and category theory meet

Qurts: Automatic quantum uncomputation by affine types with lifetime

A brief review of quantum machine learning for financial services

Compositional reversible computation

Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions

With a few square roots, quantum computing is as easy as Pi

Categories of sets with infinite addition

Ordered locales

How to bake a quantum Π

Axioms for the category of Hilbert spaces and linear contractions

Duoidally enriched Freyd categories

Universal properties of partial quantum maps

Axioms for the category of Hilbert spaces

Proceedings of the 18th International Conference on Quantum Physics and Logic

Localisable Monads

Quantum Information Effects

Sheaf representation of monoidal categories

Bennett and Stinespring, together at last

Tensor-restriction categories

Weakly measured while loops: peeking at quantum states

Compact inverse categories

Monoidal characterisation of groupoids and connectors

Ontological models for quantum theory as functors

Topos quantum theory with short posets

Automated distribution of quantum circuits

Tensor topology

Limits in dagger categories

Boolean subalgebras of orthoalgebras

Reversible effects as inverse arrows

Denotational validation of higher-order Bayesian inference

Purity through factorisation

Space in monoidal categories

Frobenius structures over Hilbert C*-modules

A convenient category for higher-order probability theory

Proceedings of the 13th International Conference on Quantum Physics and Logic

Can a quantum state over time resemble a quantum state at a single time?

Discretization of C*-algebras

Pictures of complete positivity in arbitrary dimension

The CBH characterisation theorem beyond algebraic quantum theory

Monads on dagger categories

Reversible monadic programming

Semantics for probablistic programming: higher-order functions, continuous distributions, soft constraints

The category of matroids

Proceedings of the 12th International Workshop on Quantum Physics and Logic

Categories of relations as models of quantum theory

Axiomatizing complete positivity

Domains of commutative C*-subalgebras

The many classical faces of quantum structures

Book review: Foundations of relational realism

Mixed quantum states in higher categories

Categories of quantum and classical channels

Extending obstructions to noncommutative functorial spectra

No-go theorems for functorial localic spectra of noncommutative rings

Operational theories and categorical quantum mechanics

Piecewise Boolean algebras and their domains

Characterizations of categories of commutative C*-subalgebras

Quantum realization of arbitrary joint measurability structures

Active lattices determine AW*-algebras

Quantum theory realises all joint measurability graphs

Matrix multiplication is determined by orthogonality and trace

Completely positive projections and biproducts

On the functor l²

Compositional quantum logic

Diagonalizing matrices over AW*-algebras

Relative Frobenius algebras are groupoids

Quantum physics and linguistics: a compositional, diagrammatic discourse

Completely positive classical structures and sequentializable quantum protocols

H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics

Entangled and sequential quantum protocols with dephasing

Complementarity in categorical quantum mechanics

Noncommutativity as a colimit

Bohrification of operator algebras and quantum logic

The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach

Bohrification

Quantum logic in dagger kernel categories

Coalgebraic components in a many-sorted microcosm

Intuitionistic quantum logic of an n-level system

A topos for algebraic quantum theory

Categorical quantum models and logics

Categorical semantics for Arrows

An embedding theorem for Hilbert categories

Semimodule enrichment

The principle of general tovariance

Arrows, like Monads, are Monoids

Tensegrities, of houtje-touwtje-figuren

Accurate silhouettes - do polyhedral models suffice?