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We investigate the possibility of implementing a sequence of quantum walkswhose 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 realisation with a Bose-Einstein condensate inwhich the walker's space is momentum space. Experimental problems in theprecise implementation of the coin operations for our discrete-time quantumwalks are analysed in detail. We study time-dependent phase fluctuations of thecoins as well as perturbations arising from the finite momentum width of thecondensate. We confirm the visibility of Parrondo's paradox for experimentallyavailable time scales of up to a few hundred steps of the walk.

Parrondo's paradox for discrete-time quantum walks in momentum space