The Clifford hierarchy is a nested sequence of sets quantum gates critical to achieving fault-tolerant computation. Diagonal the and 'nearly diagonal' semi-Clifford are particularly important: they admit efficient gate teleportation protocols that implement these with fewer ancillary resources such as magic states. Despite practical importance gates, many questions about their structure remain ...

We describe a five-dimensional analogue of Wigner's operator equation ${\mathbb W}_a = \lambda P_a$, where $ is the Pauli-Lubanski vector, $P_a$ energy-momentum operator, and $\lambda$ helicity massless particle. Higher dimensional generalisations are also given.