On classical capacity of Weyl channels

Grigori Gennadievich Amosov

Katarzyna Siudzińska

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.

Masanori Ohya, Dėnes Petz, Noboru Watanabe

Junaid ur Rehman, Youngmin Jeong, Jeong San Kim +1 more

Holevo capacity is the maximum rate at which a quantum channel can reliably transmit classical information without entanglement. However, calculating the Holevo capacity of arbitrary quantum channels is a nontrivial and computationally expensive task since it requires the numerical optimization over all possible input quantum states. In this paper, we consider discrete Weyl channels (DWCs) and exploit their symmetry properties to model DWC as a classical symmetric channel. We characterize lower and upper bounds on the Holevo capacity of DWCs using simple computational formulae. Then, we provide a sufficient and necessary condition where the upper and lower bounds coincide. The framework in this paper enables us to characterize the exact Holevo capacity for most of the known special cases of DWCs.

Jeffrey H. Shapiro

M. A. Antonets