Physics – Quantum Physics
Scientific paper
2011-05-05
Physics
Quantum Physics
26 pages, new section devoted to the difference between the quantum mutual information and the $\chi$-function of a quantum ch
Scientific paper
Both necessary and sufficient conditions of coincidence of the entanglement-assisted capacity and the Holevo capacity of a quantum channel are obtained. By using these conditions the equality between these capacities as well as the strict inequality between them are proved for several classes of quantum channel. In particular, it is shown that coincidence of the entanglement-assisted capacity and the Holevo capacity of a quantum channel implies that the $\chi$-essential part of this channel is entanglement-breaking (the $\chi$-essential part is defined as a restriction of a channel obtained by discarding all states useless for transmission of classical information). The above conditions and their corollaries are extended to quantum channels with linear constraints. By using these conditions it is shown that the question of coincidence of the entanglement-assisted capacity with the Holevo capacity of a constrained channel depends on the form of the constraint. Properties of the difference between the quantum mutual information and the $\chi$-function of a quantum channel are explored.
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