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 ◦ N(σ) = σ and

D(ρ | σ) ≥ D(N(ρ) | N(σ)) 2 log ||√ρRN(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 RN(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:

2017 Johannes Bausch, Toby Cubitt, and Maris Ozols
The Complexity of Translationally Invariant Spin Chains with Low Local Dimension


Sven Bachmann, Wojciech Dybalski and Pieter Naaijkens 

Lieb-Robinson Bounds, Arveson Spectrum and Haag-Ruelle Scattering Theory for Gapped Quantum Spin Systems


Ira Herbst and Juliane Rama

Instability of Pre-Existing Resonances Under a Small Constant Electric Field


David Damanik, Jake Fillman and Anton Gorodetski

Continuum Schrödinger Operators Associated With Aperiodic Subshifts


Dean Baskin

Strichartz Estimates on Asymptotically de Sitter Spaces


Semyon Dyatlov

Asymptotic Distribution of Quasi-Normal Modes for Kerr–de Sitter Black Holes


László Erdős and Antti Knowles

Quantum Diffusion and Delocalization for Band Matrices with General Distribution


J.-M. Barbaroux, T. Chen, V. Vougalter and S. Vugalter

Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED


D. Dolgopyat and B. Fayad

Unbounded Orbits for Semicircular Outer Billiard


P. Bálint and I. P. Tóth

Exponential Decay of Correlations in Multi-Dimensional Dispersing Billiards


Fabien Vignes-Tourneret

Renormalization of the Orientable Non-commutative Gross–Neveu Model


Giuseppe Benfatto, Alessandro Giuliani and Vieri Mastropietro

Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures


Alexander V. Sobolev

Integrated Density of States for the Periodic Schrödinger Operator in Dimension Two


Nandor Simanyi

Proof of the Ergodic Hypothesis for Typical Hard Ball Systems


Alessandro Pizzo

One-particle (improper) States in Nelson’s Massless Model


Lorenzo Bertini, Stella Brassesco, Paolo Buttà, and Errico Presutti

Stochastic Phase Field Equations: Existence and Uniqueness


Galina Perelman

On the Formation of Singularities in Solutions of the Critical Nonlinear Schrödinger Equation


Michael T. Anderson and to Gueorgui Popov

On the Structure of Solutions to the Static Vacuum Einstein Equations , Invariant Tori, Effective Stability, and Quasimodes with Exponentially Small Error Terms