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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…
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 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…