19 citations · 38 across the 13 of their papers we have counts for
14 papers
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…
Supermaps on generalised theories
Matt Wilson, James Hefford, Timothée Hoffreumon
Categorical supermaps generalise higher-order quantum operations from finite-dimensional quantum theory to arbitrary circuit theories. In this paper, we establish the Yoneda lemma…
Decoherence to quantum theory from a causally-indefinite post-quantum theory
James Hefford, Matt Wilson
We find a process satisfying the axioms of hyper-decoherence which produces standard quantum theory from the theory of quantum boxes (higher-order quantum theory with the non-signa…
A BV-Category of Spacetime Interventions
James Hefford, Matt Wilson
We use the Chu construction to functorially build BV-categories from duoidal categories, demonstrating that candidate models of BV-logic can be cofreely constructed from a fragment…
A Profunctorial Semantics for Quantum Supermaps
James Hefford, Matt Wilson
We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader f…
Optics for Premonoidal Categories
James Hefford, Mario Román
We further the theory of optics or "circuits-with-holes" to encompass premonoidal categories: monoidal categories without the interchange law. Every premonoidal category gives rise…
The Produoidal Algebra of Process Decomposition
Matt Earnshaw, James Hefford, Mario Román
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal co…
On the Pre- and Promonoidal Structure of Spacetime
James Hefford, Aleks Kissinger
The notion of a joint system, as captured by the monoidal (a.k.a. tensor) product, is fundamental to the compositional, process-theoretic approach to physical theories. Promonoidal…
Coend Optics for Quantum Combs
James Hefford, Cole Comfort
We compare two possible ways of defining a category of 1-combs, the first intensionally as coend optics and the second extensionally as a quotient by the operational behaviour of 1…
CPM Categories for Galois Extensions
James Hefford, Stefano Gogioso
By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalis…
The Safari of Update Structures: Visiting the Lens and Quantum Enclosures
Matthew Wilson, James Hefford, Guillaume Boisseau +1
We build upon our recently introduced concept of an update structure to show that it is a generalisation of very-well-behaved lenses, that is, there is a bijection between a strict…
Categories of Semantic Concepts
James Hefford, Vincent Wang, Matthew Wilson
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from Gärdenfors semanti…
Hyper-decoherence in Density Hypercubes
James Hefford, Stefano Gogioso
We study hyper-decoherence in three operational theories from the literature, all examples of the recently introduced higher-order CPM construction. Amongst these, we show the theo…
Optimal local unitary encoding circuits for the surface code
Oscar Higgott, Matthew Wilson, James Hefford +4
The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006)…