52 citations · 72 across the 12 of their papers we have counts for
12 papers
Monoidal su-categories
Matt Wilson, Giulio Chiribella
We introduce monoidal su-categories, an abstract categorical notion of single-input higher-order process over a monoidal category. The definition separates a base category C of low…
Categories of tagged lenses
Matt Wilson
To better understand the landscape of well-behavedness laws for lenses on strict Cartesian symmetric monoidal categories, we define tagged lenses. We prove that tagged lenses form…
Higher-Order Quantum Objects are Strong Profunctors
Matt Wilson, James Hefford
We explore the sense in which the existing constructions for higher-order maps on quantum theory based on causality constraints and compositionality constraints respectively, coinc…
On the Origin of Linearity and Unitarity in Quantum Theory
Matt Wilson, Nick Ormrod
We reconstruct the transformations of quantum theory using a physically motivated postulate. This postulate states that transformations should be locally applicable, and recovers t…
Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension
Matt Wilson, Giulio Chiribella
We provide a construction for holes into which morphisms of abstract symmetric monoidal categories can be inserted, termed the polyslot construction pslot[C], and identify a sub-cl…
Quantum Supermaps are Characterized by Locality
Matt Wilson, Giulio Chiribella, Aleks Kissinger
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps t…
A Mathematical Framework for Transformations of Physical Processes
Matt Wilson, Giulio Chiribella
We observe that the existence of sequential and parallel composition supermaps in higher order theories of transformations can be formalised using enriched category theory. Encoura…
Generalised tensors and traces
Pablo Arrighi, Amélia Durbec, Matt Wilson
Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations b…
Composable constraints
Matt Wilson, Augustin Vanrietvelde
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint…
Quantum networks theory
Pablo Arrighi, Amélia Durbec, Matt Wilson
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so t…
Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders
Giulio Chiribella, Matt Wilson, H. F. Chau
Completely depolarising channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-def…
A Diagrammatic Approach to Information Transmission in Generalised Switches
Matt Wilson, Giulio Chiribella
The quantum switch is a higher-order operation that takes as an input two quantum processes and combines them in a coherent superposition of two alternative orders. Here we provide…