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

preprint2018arXivOpen access

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.

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