# AHP Prizes and Distinguished Papers

Each year a prize founded by Birkhäuser is awarded for the most remarkable paper published in the journal Annales Henri Poincaré. The winners of the AHP prize are selected by the Editorial Board. Since 2008, the AHP executive board decided to award also distinguished papers. All papers are freely accessible online for one year!

**The AHP Prize 2018 was awarded to Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, and Andreas Winter for the paper **

Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy

The states in quantum mechanics correspond to self-adjoint, positive semideﬁnite trace-class operators of trace 1. Channels are completely positive trace preserving linear maps. The famous “*data processing inequality*” states that relative entropy between two states *ρ* and *σ* can never increase under the action of the same channel *N**D*(*ρ* | *σ*) ≥ *D*(*N*(*ρ*) | *N*(*σ*)).

Junge et al. strengthened this inequality signiﬁcantly by estimating the remainder term. For any state *σ* and any channel *N* they provide the explicit construction of a “*universal*” recovery map *R* such that *R *◦ *N*(*σ*) = *σ* and*D*(*ρ* | *σ*) ≥ *D*(*N*(*ρ*) | *N*(*σ*)) *− *2 log ||√*ρ*√*R*◦*N*(*ρ*)||1* *

for any state *ρ* such that Ran(*ρ*) ⊂ Ran(*σ*). The trace norm appearing on the right-hand side is a ﬁdelity and is usually interpreted as a measure of the distance between *ρ* and its recovery *R* ◦ *N*(*ρ*). In addition to the general aspects of quantum information theory, the results make a signiﬁcant contribution to information theoretic characterization of approximate quantum error correction.

**Previous AHP Prize winners:**