Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator

Abstract

We study a 2D disordered discrete-time quantum walk (QW) based on 1D generalized elephant QW where an entangling coin operator is assumed. We show that considering a given disorder in one direction, it is possible to control the degree of spreading and entanglement in the other direction. This observation helps assert that the random QWs of this ilk serve as a controllable decoherence channel with the degree of randomness being the tunable parameter and highlight the role of dimensionality in quantum systems regarding information and transport.