Classical and entanglement-assisted capacity of a qubit depolarizing memory channel

We study the classical and entanglement-assisted capacity of a forgetful quantum memory channel that randomly switches between two qubit depolarizing channels. We show that when the input consists of two qubits then depending on channel parameters either the maximally entangled input states or product input states achieve the two-use classical capacity. We conjecture that as the number of input qubits is increased the classical capacity approaches the product state capacity for all values of the parameters. We also derive an expression for the entanglement-assisted classical capacity of this quantum memory channel in terms of the entropy rate of a Markov chain.