# CPM Categories for Galois Extensions

@article{Hefford2021CPMCF, title={CPM Categories for Galois Extensions}, author={James Hefford and Stefano Gogioso}, journal={Electronic Proceedings in Theoretical Computer Science}, year={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 quantum-to-classical transition. Analogously to the quantum-to-classical case, these decoherences reduce the degrees of freedom in physical systems, while at the same time restricting the fields over which the systems are defined. These theories possess fully fledged operational semantics, allowing…

## References

SHOWING 1-10 OF 45 REFERENCES

### Two Roads to Classicality

- Mathematics
- 2017

Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two…

### Higher-order CPM Constructions

- MathematicsElectronic Proceedings in Theoretical Computer Science
- 2019

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,…

### Categories of quantum and classical channels

- MathematicsQuantum Inf. Process.
- 2016

A construction that turns a category of pure state spaces and operators into a categories of observable algebras and superoperators is introduced, providing elegant abstract notions of preparation and measurement.

### Axiomatizing complete positivity

- PhysicsArXiv
- 2015

There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps, and this work extends this axiomatization to the latter by introducing decoherence structures.

### The Topology of Quantum Algorithms

- Computer Science
- 2012

A categorical topological semantics is used to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms, giving for the first time a satisfying high-level explanation for why these procedures work.

### Environment and classical channels in categorical quantum mechanics

- Computer ScienceLog. Methods Comput. Sci.
- 2010

We present a both simple and comprehensive graphical calculus for quantum computing. We axiomatize the notion of an environment, which together with the axiomatic notion of classical structure…

### A categorical semantics of quantum protocols

- Computer ScienceProceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
- 2004

This paper focuses on quantum information protocols, which exploit quantum-mechanical effects in an essential way and form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation.

### Categories for Quantum Theory

- Physics
- 2019

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to…

### 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.

### 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…