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We investigate the question of optimal input ensembles for memory channelsand construct a rather large class of Pauli channels with correlated noisewhich can be studied analytically with regard to the entanglement of theiroptimal input ensembles. In a more detailed study of a subclass of thesechannels, the complete phase diagram of the two-qubit channel, which showsthree distinct phases is obtained. While increasing the correlation generallychanges the optimal state from separable to maximally entangled states, this isdone via an intermediate region where both separable and maximally entangledstates are optimal. A more concrete model, based on random rotations of theerror operators which mimic the behavior of this subclass of channels is alsopresented.

New Phase Transitions in Optimal States for Memory Channels