Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Recently, it was introduced a generalization of a nonstandard step operator named the elephant quantum walk (EQW). With proper statistical distribution for the steps, that generalized EQW (gEQW) can be tuned to exhibit a myriad of dynamical scaling behavior ranging from standard diffusion to %and superdiffusion to ballistic and hyperballistic spreading. In this work, we study the influence of the statistics of the step size and the delocalization of the initial states on the entanglement entropy of the coin. Our results show that the gEQW generates maximally entangled states for almost all initial coin states and coin operators considering initially localized walkers and for the delocalized ones, taking the proper limit, the same condition is guaranteed. Differently from all the previous protocols that produce highly entangled states via QWs, this model is not upper-bounded by ballistic spreading and hence opens novel prospects for applications of dynamically disordered QWs as a robust maximal entanglement generator in programmable setups that ranges from slower-than-ballistic to faster-than ballistic.