Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
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Strengthened monotonicity.pdf
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Author(s)
Sutter, David
Tomamichel, Marco
Harrow, Aram W
Date Issued
March 2016
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Sutter, David; Tomamichel, Marco and Harrow, Aram W. “Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map.” IEEE Transactions on Information Theory 62, no. 5 (May 2016): 2907–2913.
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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1109/tit.2016.2545680
