No-Concentrating Theorem of Pure Entangled States

Suppose two distant observers Alice and Bob share a pure biparticle entangled state secretly chosen from a set, it is shown that Alice (Bob) can probabilistic concentrate the state to a maximally entangled state by applying local operations and classical communication (LQCC) if and only if the states in the set share the same marginal density operator for her (his) subsystem. Applying this result, we present probabilistic superdense coding and show that perfect purification of mixed state is impossible using only LQCC on individual particles.