Controlling quantum random walk with a step-dependent coin

• Published in: New Journal of Physics
• Main Authors: S Panahiyan, S Fritzsche
• Format: Article
• Language: English
• Published: IOP Publishing 2018-01-01
• Subjects: quantum random walk; quantum information processing; Shannon entropy
• Online Access: https://doi.org/10.1088/1367-2630/aad899

We report on the possibility of controlling quantum random walks (QWs) with a step-dependent coin (SDC). The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC.