Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Monotonicity of a relative Renyi entropy

Rupert L. Frank, Elliott, H. Lieb

Published Jan 1, 2013• 177 citations
OpenAlex

Abstract

We show that a recent definition of relative R'enyi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of M"uller-Lennert et al.

Related papers

Monotonicity of a relative Rényi entropy

Rupert L. Frank, Élliott H. Lieb

We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller-Lennert et al. [“On quantum Rényi entropies: A new definition, some properties,” J. Math. Phys. 54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].

arXiv:1306.5358•Journal of Mathematical Physics•Dec 1, 2013•218 citations

On Uhlmann's proof of the Monotonicity of the Relative Entropy

Juan Manuel Pérez-Pardo

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful examples are given.

arXiv:2210.13093•Oct 24, 2022•0 citations

A new proof for monotonicity of sandwiched Renyi relative entropy

wang you le, Luo Maokang, DENG Ke

Itis well known that in quantum information quantum relative is monotonically decreasing under the completely positive and trace-preserving maps. For a new proposed sandwiched R\'enyi quantum relative, a map that is linear trace-preserving and whose Hilber-Schmidt adjoint map satisfies Schwarz inequality, monotonicity still holds. We give a new proof of monotonicity of sandwiched R\'enyi relative entropy for $\alpha\in[\frac{1}{2},1)$. The proof is based on complex interplotation techniques, which already has been used to prove monotonicity under trace-preserving and positive map for $\alpha\in(1,\infty)$.

•Jan 1, 2018•0 citations

On Uhlmann’s Proof of the Monotonicity of the Relative Entropy

Juan Manuel Pérez-Pardo

This chapter presents in a self-contained way A. Uhlmann's celebrated theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The theorem is presented in its more general form and meaningful examples are given.

WORLD SCIENTIFIC eBooks•Apr 1, 2023•1 citation

Particles, Fields and Topology

T. R. Govindarajan, Giuseppe Marmo, V. P. Nair +3 more

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps.The Theorem is presented in its more general form and meaningful examples are given.

WORLD SCIENTIFIC eBooks•Nov 3, 2022•1 citation

Maps on positive operators preserving Rényi type relative entropies and maximal f-divergences

Marcell Gaál, Gergő Nagy

arXiv:1703.05244•Letters in Mathematical Physics•Oct 26, 2017•2 citations
Itis well known that in quantum information quantum relative is monotonically decreasing under the completely positive and trace-preserving maps. For a new proposed sandwiched R\'enyi quantum relative, a map that is linear trace-preserving and whose Hilber-Schmidt adjoint map satisfies Schwarz inequality, monotonicity still holds. We give a new proof of monotonicity of sandwiched R\'enyi relative entropy for α∈[12,1)\alpha\in[\frac{1}{2},1)α∈[21​,1). The proof is based on complex interplotation techniques, which already has been used to prove monotonicity under trace-preserving and positive map for α∈(1,∞)\alpha\in(1,\infty)α∈(1,∞).