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

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

“…Thus, this work also makes a contribution in such subject. In a previous work [31] the entanglement generation in the 1D gEQW was extensively studied, where it was demonstrated that this type of walk generates maximally entangled coin states for almost all initial parameters. Adding the above mentioned results, the present work shows that the gEQW also has the potential to generate highly entangled coin states in 2D settings, while also maintaining the ability of controlling the walker spreading rate, something that in the context of other types of random QWs is not possible.…”

“…We interpret this unitary random evolution as an evolution in which the environment selects a random step at each time instant, e.g. because of an imperfect physical implementation of the QW, followed by a measurement from the experimenters [31]. The two-dimensional gEQW model we propose is a modified version of the 2D DTQW described previously (see figure 3).…”

“…Within this context, the introduction of a memory model [23]-which at odds with the Markovianity of the canonical QW-has set forth the possibility of introducing a random QW model yielding a broad diffusion behavior ranging from normal to hyper-ballistic [24]. Moreover, it was recently shown [31] that such a class of QWs generates maximally entangled states for almost all initial coin states and coin operators whether the walker is at first localized or not. One the other hand, there are one-dimensional QWs where dynamical disorder is introduced in the coin operator [32][33][34][35] and the same phenomenon is observed, something that was experimentally verified recently in a photonic setup [36].…”