N-dimensional alternate coined quantum walks from a dispersion-relation perspective

We suggest an alternative definition of N-dimensional coined quantum walk by generalizing a recent proposal [Di Franco et al., Phys. Rev. Lett. 106, 080502 (2011)]. This N-dimensional alternate quantum walk, AQW(N), in contrast with the standard definition of the N-dimensional quantum walk, QW(N), requires only a coin qubit. We discuss the quantum diffusion properties of AQW(2) and AQW(3) by analyzing their dispersion relations that reveal, in particular, the existence of diabolical points. This allows us to highlight interesting similarities with other well-known physical phenomena. We also demonstrate that AQW(3) generates considerable genuine multipartite entanglement. Finally, we discuss the implementability of AQW(N)