On lower semicontinuity of the entropic disturbance and its applications in quantum information theory

M. E. Shirokov ; A. S. Holevo

Izvestiya. Mathematics , Tome 81 (2017) no. 5, pp. 1044-1060.

Résumé

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.

Détail

Keywords: von Neumann entropy, $\chi$-quantity, ensemble of quantum states, quantum channel, classical capacity.

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