  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 realisation 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 analysed 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.
