Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo’s paradox). In particular, we have in mind an experimental realization with a Bose–Einstein condensate in which the walker’s space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analyzed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo’s paradox for experimentally available time scales of up to a few hundred steps of the walk.