Quantum capacity of dephasing channels with memory

We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode environment of oscillators. While in the first model, the maximization is achieved for the maximally mixed input state, in the latter it is convenient to exploit the presence of a decoherence-protected subspace generated by memory effects. We explicitly compute the quantum channel capacity for the first model while numerical simulations suggest a lower bound for the latter. In both cases memory effects enhance the coherent information. We present results valid for arbitrary input size.