  We observe the onset of non-ergodicity from ballistic propagation of a
two-body bound state in an interacting discrete-time quantum walk (DTQW) due to
time-dependent disorder in the interaction. The effect of the disorder on the
two-body state can be interpreted as Anderson-type localisation in a projected
DTQW, but without saturation of entanglement entropy. We characterise the
two-body localisation in terms of the rate of growth of entanglement entropy
and compute the localisation length. We find indications for two distinct
growth laws for the entanglement: a logarithmic law in the delocalised phase
and a double logarithmic law in the localised phase. We discuss similarities
with many-body localisation (MBL).
