Mutual Information of Pauli Channels with Correlated Noise

A general formula for the mutual information of the Pauli channels with memory modelled by correlated noise is derived. It is shown that the mutual information depends on the channel shrinking factor, the input state parameter and the channel memory coefficient. The analyses based on the general formula reveal that the entanglement is always a useful resource to enhance the mutual information of some Pauli channels, such as the bit flip
channel and the bit-phase flip channel. Our analyses also show that the entanglement is not advantageous to the reliable transmission of classical information for some Pauli channels at any time, such as the phase flip channel and the phase damping channel.