Geometric inequalities from phase space translations

DOI10.1063/1.4974224zbMath1376.81013arXiv1606.08603OpenAlexW3101250232MaRDI QIDQ2963289

Robert Koenig, Stefan Huber, Anna Vershynina

Publication date: 13 February 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08603

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Markov semigroups and applications to diffusion processes (47D07) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Measures of information, entropy (94A17) Isoperimetric problems for polytopes (52B60) Channel models (including quantum) in information and communication theory (94A40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (8)

The entropy power inequality with quantum conditioning ⋮ Coherent state coding approaches the capacity of non-Gaussian bosonic channels ⋮ An oscillator with position-dependent mass exposed to a thermal bosonic bath ⋮ Gaussian optimizers for entropic inequalities in quantum information ⋮ Contractivity properties of a quantum diffusion semigroup ⋮ Curvature-dimension conditions for symmetric quantum Markov semigroups ⋮ Enhancing estimation precision of parameter for a two-level atom with circular motion ⋮ The conditional entropy power inequality for quantum additive noise channels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• Superadditivity of Fisher's information and logarithmic Sobolev inequalities
• Brascamp--Lieb inequalities for non-commutative integration
• Entropy and the central limit theorem
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Inequalities in Fourier analysis
• Proof of an entropy conjecture of Wehrl
• Hypercontractivity in noncommutative \(L_1\) spaces
• Hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup
• Convex trace functions and the Wigner-Yanase-Dyson conjecture
• Relative entropy convergence for depolarizing channels
• Schwartz operators
• Entropy power inequalities for qudits
• Contractivity properties of a quantum diffusion semigroup
• Corrections to “The Entropy Power Inequality for Quantum Systems” [Mar 14 1536-1548]
• Passive States Optimize the Output of Bosonic Gaussian Quantum Channels
• Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator
• The Entropy Power Inequality for Quantum Systems
• On a quantum entropy power inequality of Audenaert, Datta, and Ozols
• On the similarity of the entropy power inequality and the Brunn- Minkowski inequality (Corresp.)
• Quantum harmonic analysis on phase space
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• A simple proof of the entropy-power inequality
• A new entropy power inequality
• Information theoretic inequalities
• A proof of the Fisher information inequality via a data processing argument
• A short proof of the "concavity of entropy power"
• The conditional entropy power inequality for Gaussian quantum states
• The convolution inequality for entropy powers
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Elements of Information Theory

This page was built for publication: Geometric inequalities from phase space translations