Harrow, Aram W.
- Working Paper
The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a "recovery map" that exactly reverses the effects of the quantum channel on both states. In this paper we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the quantum channel on the second state. As a special case we reproduce recent lower bounds on the conditional mutual information such as the one proved in [Fawzi and Renner, Commun. Math. Phys., 2015]. Our proof only relies on elementary properties of pinching maps and the operator logarithm Show more
Journal / seriesarXiv
Organisational unit03781 - Renner, Renato
NotesSubmitted on 1 July 2015, Last revised 9 December 2015. See also: http://e-citations.ethbib.ethz.ch/view/pub:178023.
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