Entanglement and optimal strings of qubits for memory channels

We investigate the problem of enhancement of mutual information by encoding classical data into entangled input states of arbitrary length and show that while there is a threshold memory or correlation parameter beyond which entangled states outperform the separable states, resulting in a higher mutual information, this memory threshold increases toward unity as the length of the string increases. These observations imply that encoding classical data into entangled states may not enhance the classical capacity of quantum channels.