Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map

Jump to other IT Society Websites:

Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map


Creation Date: Jul 10, 2016

Published In: Jul 2016

Paper Type: Conference Paper

Book Title: Proceedings of the 2016 IEEE International Symposium on Information Theory

Address: Barcelona, Spain


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.

IEEE Explore link:

Award(s) Received:
Latest News
IEEE TV Profiles and Interviews
The First Workshop on the Age of Information - Call For Papers
ITSoc BoG contribution for newsletter

Upcoming Events

NSF Workshop on Low-Latency Wireless Random-Access at MIT
02-03 Nov 2017 | MIT Grier Room 34-401, 50 Vassar Street, Cambridge, MA, USA
2017 IEEE Information Theory Workshop
06-10 Nov 2017 | Kaohsiung Exhibition Center, Kaohsiung, Taiwan
Fano Memorial in Turin
10 Nov 2017 | Turin, Salone d'onore del Castello del Valentino.