  We analytically investigate the recently proposed and implemented
discrete-time quantum walk based on a kicked Bose-Einstein condensate. We
extend previous work on the effective dynamics by taking into account
spontaneous emission due to the kicking light. Spontaneous emission affects
both the internal and external degrees of freedom, arising from the
entanglement between them during the walk dynamics. The result is a measurable
degrading of the experimental walk signal that we characterise.
