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

## 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.

## Keywords

Quantum theory Categorical probabilistic theories Higher-order interference Hyperdecoherence## Notes

### Acknowledgements

SG is supported by a grant on Quantum Causal Structures from the John Templeton Foundation. CMS was supported in the writing of this paper by the Engineering and Physical Sciences Research Council (EPSRC) through the doctoral training grant 1652538 and by the Oxford-Google DeepMind graduate scholarship. CMS is currently supported by the Pacific Institute for the Mathematical Sciences (PIMS) and from a Faculty of Science Grand Challenge award at the University of Calgary. This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.

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