  A new family of polarized ensembles of random pure states is presented. These
ensembles are obtained by linear superposition of two random pure states with
suitable distributions, and are quite manageable. We will use the obtained
results for two purposes: on the one hand we will be able to derive an
efficient strategy for sampling states from isopurity manifolds. On the other,
we will characterize the deviation of a pure quantum state from separability
under the influence of noise.
