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

TL;DR

This paper introduces an N-dimensional alternate quantum walk using only a coin-qubit, analyzes its diffusion properties and entanglement, and discusses its physical implementation, revealing novel dispersion relation features.

Contribution

It proposes a new N-dimensional quantum walk model based on a simplified coin system and explores its physical and entanglement properties.

Findings

Dispersion relations show diabolical points in AQW_2 and AQW_3.

AQW_3 generates genuine multipartite entanglement.

The model's implementability is discussed.

Abstract

We propose an alternative definition of an 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 genuine multipartite entanglement. Finally we discuss the implementability of AQW_N.