Density Hypercubes, Higher Order Interference and Hyper-Decoherence: a Categorical Approach

TL;DR

This paper introduces a new categorical probabilistic framework for density hypercubes, demonstrating higher-order interference and hyperdecoherence, which bridges to quantum theory via the Karoubi envelope.

Contribution

It develops a novel categorical theory of density hypercubes using double-dilation, revealing higher-order interference and hyperdecoherence mechanisms.

Findings

Displays interference of order up to four in multi-slit experiments

Possesses hyperdecoherence maps for recovering quantum theory

Provides a categorical construction linking hypercubes to quantum mechanics

Abstract

In this work, we use the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes. By considering multi-slit experiments, we show that the theory displays higher-order interference of order up to fourth. We also show that the theory possesses hyperdecoherence maps, which can be used to recover quantum theory in the Karoubi envelope.