标题： $Δ_χ$量的下半连续性及其在量子信息理论中的应用 显示英文标题

标题： Lower semicontinuity of $Δ_χ$-quantity and its applications in quantum information theory

摘要： We consider a new entropic characteristic of a quantum channel -- the $\Delta_\chi$-quantity, defined as difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel. We prove that it is lower semicontinuous on the natural set of its definition. We establish a number of useful corollaries of this property, in particular, we prove the continuity of the output $\chi$-quantity and the existence of $\chi$-optimal ensemble for any quantum channel under the energy-type input constraint. 显示英文摘要

摘要： We consider a new entropic characteristic of a quantum channel -- the $\Delta_\chi$-quantity, defined as difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel. We prove that it is lower semicontinuous on the natural set of its definition. We establish a number of useful corollaries of this property, in particular, we prove the continuity of the output $\chi$-quantity and the existence of $\chi$-optimal ensemble for any quantum channel under the energy-type input constraint.