Coend Optics for Quantum Combs

by   James Hefford, et al.

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-combs on lower-order maps. We show that there is a full and bijective on objects functor quotienting the intensional definition to the extensional one and give some sufficient conditions for this functor to be an isomorphism of categories. We also show how the constructions for 1-combs can be extended to produce polycategories of n-combs with similar results about when these polycategories are equivalent. The extensional definition is of particular interest in the study of quantum combs and we hope this work might produce further interest in the usage of optics for modelling these structures in quantum theory.


page 1

page 2

page 3

page 4


Quantum Operads

The most standard description of symmetries of a mathematical structure ...

Universal Properties in Quantum Theory

We argue that notions in quantum theory should have universal properties...

Quasi-Cyclic Constructions of Quantum Codes

We give sufficient conditions for self-orthogonality with respect to sym...

Pseudorandom States, Non-Cloning Theorems and Quantum Money

We propose the concept of pseudorandom states and study their constructi...

Causality in Higher Order Process Theories

Quantum supermaps provide a framework in which higher order quantum proc...

Spectral Presheaves, Kochen-Specker Contextuality, and Quantale-Valued Relations

In the topos approach to quantum theory of Doering and Isham the Kochen-...

Please sign up or login with your details

Forgot password? Click here to reset