CPM Categories for Galois Extensions

TL;DR

This paper introduces an infinite hierarchy of probabilistic theories based on generalized CPM categories, exploring their decoherence structures and implications for quantum-to-classical transition.

Contribution

It generalizes the CPM construction to develop new probabilistic theories with decoherence structures, expanding understanding of quantum-classical boundaries.

Findings

Develops an infinite hierarchy of probabilistic theories

Shows how decoherence reduces system degrees of freedom

Provides operational semantics for the new theories

Abstract

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 both categorical and GPT-style approaches to their study.