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

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