Classical capacity of generalized Pauli channels

Abstract

Finding the classical capacity of a quantum channel is not easy, yet we are able to analytically calculate this capacity for new channels. We analyze the bounds of the Holevo capacity and classical capacity for the generalized Pauli channels. In particular, by generalizing earlier results for the Weyl channels, we obtain the lower and upper bounds of the Holevo capacity and show that, if these bounds coincide, the Holevo capacity is weakly additive. We also prove the weak additivity of the lower bound. Two new examples of the generalized Pauli channels with known classical capacity are presented. Finally, we relate the change rate of the classical capacity to the P-divisibility of Pauli channels.