  Overcoming repeaterless bounds for the secret key rate capacity of quantum
key distribution protocols is still a challenge with current technology. D.
Luong et al. [Applied Physics B 122, 96 (2016)] proposed a protocol to beat a
repeaterless bound using one pair of quantum memories. However, the required
experimental parameters for the memories are quite demanding. We extend the
protocol with multiple pairs of memories, operated in a parallel manner to
relax these conditions. We quantify the amount of relaxation in terms of the
most crucial memory parameters, given the number of applied memory pairs. In
the case of high-loss channels we found that adding only a few pair of memories
can make the crossover possible.
