Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map

Publisher:
IEEE
Publication Type:
Journal Article
Citation:
IEEE Transactions on Information Theory, 2016, 62 (5), pp. 2907 - 2913
Issue Date:
2016-05
Full metadata record
Files in This Item:
Filename Description Size
1507.00303v3.pdfSubmitted Version227.52 kB
Adobe PDF
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 by Fawzi and Renner. Our proof only relies on the elementary properties of pinching maps and the operator logarithm
Please use this identifier to cite or link to this item: