  We analyze the quantum query complexity of sorting under partial information.
In this problem, we are given a partially ordered set $P$ and are asked to
identify a linear extension of $P$ using pairwise comparisons. For the standard
sorting problem, in which $P$ is empty, it is known that the quantum query
complexity is not asymptotically smaller than the classical
information-theoretic lower bound. We prove that this holds for a wide class of
partially ordered sets, thereby improving on a result from Yao (STOC'04).
