7 papers
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…
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…
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…
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…
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…
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…