  We find a universal lower bound on locally accessible information for
arbitrary bipartite quantum ensembles, when one of the parties is
two-dimensional. In higher dimensions and in higher number of parties, the
lower bound is on accessible information by separable operations. We show that
for any given density matrix (of arbitrary number of parties and dimensions),
there exists an ensemble, the ''Scrooge ensemble'', which averages to the given
density matrix and whose locally accessible information saturates the lower
bound. Moreover, we use this lower bound along with a previously obtained upper
bound to obtain bounds on the yield of singlets in distillation protocols that
involve local distinguishing.
