Geodesic
On lower semicontinuity of the entropic disturbance and its applications in quantum information theory
Izvestiya. Mathematics , Tome 81 (2017) no. 5, pp. 1044-1060

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We consider an important characteristic of a quantum channel called the entropic disturbance. It is defined as the difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel. We prove the lower semicontinuity of the entropic disturbance for any infinite-dimensional quantum channel on its natural domain. A number of useful corollaries of this property are established, in particular, the existence of a $\chi$-optimal ensemble for any quantum channel and the continuity of the output $\chi$-quantity under the energy-type input constraint.
Keywords: von Neumann entropy, $\chi$-quantity, ensemble of quantum states, quantum channel, classical capacity. 
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     author = {M. E. Shirokov and A. S. Holevo},
     title = {On lower semicontinuity of the entropic disturbance and its applications in quantum information theory},
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M. E. Shirokov; A. S. Holevo. On lower semicontinuity of the entropic disturbance and its applications in quantum information theory. Izvestiya. Mathematics , Tome 81 (2017) no. 5, pp. 1044-1060. http://geodesic.mathdoc.fr/item/IM2_2017_81_5_a5/