# Higher-order CPM Constructions

@article{Gogioso2018HigherorderCC, title={Higher-order CPM Constructions}, author={Stefano Gogioso}, journal={Electronic Proceedings in Theoretical Computer Science}, year={2018} }

We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can be characterised by seeing the construction as an algebra for an appropriate monad. We provide several examples of the construction, connecting to previous work on the CPM construction and on categorical probabilistic theories, as well as upcoming work on…

## 4 Citations

### CPM Categories for Galois Extensions

- PhilosophyElectronic Proceedings in Theoretical Computer Science
- 2021

By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional…

### Fantastic Quantum Theories and Where to Find Them

- Mathematics
- 2017

We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive…

### Hyper-decoherence in Density Hypercubes

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

This work demonstrates the existence of a probabilistic hyper-decoherence of density hypercubes to quantum systems and calculate the associated hyper-phase group.

### Density Hypercubes, Higher Order Interference and Hyper-decoherence: A Categorical Approach

- Computer ScienceQI
- 2018

This work uses the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes and shows that the theory displays higher-order interference of order up to fourth.

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