  We numerically investigate the encoding and retrieval processes for a quantum
memory realized in a semiconductor quantum dot, by focusing on the effect of
inhomogeneously polarized nuclear spins whose polarization depends on the local
hyperfine coupling strength. We find that the performance of the quantum memory
is significantly improved by the inhomogeneous nuclear polarization, as
compared to the homogeneous one. Moreover, the narrower the nuclear
polarization distribution is, the better the performance of the quantum memory
is. We ascribe the performance improvement to the full harnessing of the highly
polarized and strongly coupled nuclear spins, by carefully studying the entropy
change of individual nuclear spins during encoding process. Our results shed
new light on the implementation of a quantum memory in a quantum dot.
