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