  We establish contact between the delocalization properties of pure quantum
states, as quantified by their number of principal components, and the average
generalized entanglement properties, as quantified by purity measures relative
to different observable sets. We find that correlations between products of
state vector components with respect to Hamming distance play an important role
in the structure of subsystem-based purity measures. In particular, we derive
general conditions under which the amount of global multipartite entanglement
relates to the inverse participation ratio averaged over a maximal set of
mutually unbiased product bases. Furthermore, we provide a method for computing
the expected amount of generalized entanglement with respect to an arbitrary
observable set for random pure states. Specific examples and an explicit
application to a disordered quantum spin chain are discussed.
