Hyper-decoherence in Density Hypercubes

We study hyper-decoherence in three operational theories from the literature, all examples of recently introduced higher-order CPM construction. Amongst these, we show theory density hypercubes to be richest terms post-quantum phenomena. Specifically, demonstrate existence a probabilistic quantum systems and calculate associated hyper-phase group. This makes significant foundational interest, as an example which side-steps recent no-go result original unforeseen way, while at same time displaying fully fledged semantics.