A criterion for coincidence of the entanglement-assisted classical capacity and the Holevo capacity of a quantum channel

Abstract

It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the above-mentioned capacities of a quantum channel implies that the $\chi$-essential part of this channel is a c-q channel (the $\chi$-essential part is a restriction of a channel obtained by discarding all input states useless for transmission of classical information). The above observations are generalized to infinite dimensional quantum channels with linear constraints by using the obtained conditions for coincidence of the quantum mutual information and the constrained Holevo capacity.

17 pages, generalizations to infinite dimensional quantum channels with linear constraints have been added. arXiv admin note: text overlap with arXiv:1106.3297

References in corpus (2)

• Majorization theory approach to the Gaussian channel minimum entropy conjecture
• On approximation of quantum channels