  Multiparty quantum states are useful for a variety of quantum information and
computation protocols. We define a multiparty entanglement measure based on
local measurements on a multiparty quantum state, and an entanglement measure
averaged on the post-measurement ensemble. Using the generalized geometric
measure as the measure of multipartite entanglement for the ensemble, we
demonstrate, in the case of several well-known classes of multipartite pure
states, that the localized multipartite entanglement can exceed the
entanglement present in the original state. We also show that measurement over
multiple parties may be beneficial in enhancing localizable multipartite
entanglement. We point out that localizable generalized geometric measure
faithfully signals quantum critical phenomena in well-known quantum spin models
even when considerable finite-size effect is present in the system.
