We survey the state of the art for the proof of the quantum Gaussian
optimizer conjectures of quantum information theory. These fundamental
conjectures state that quantum Gaussian input states are the solution to
several optimization problems involving quantum Gaussian channels. These
problems are the quantum counterpart of three fundamental results of functional
analysis and probability: the Entropy Power Inequality, the sharp Young's
inequality for convolutions and the theorem "Gaussian kernels have only
Gaussian maximizers". Quantum Gaussian channels play a key role in quantum
communication theory: they are the quantum counterpart of Gaussian integral
kernels and provide the mathematical model for the propagation of
electromagnetic waves in the quantum regime. The quantum Gaussian optimizer
conjectures are needed to determine the maximum communication rates over
optical fibers and free space. The restriction of the quantum-limited Gaussian
attenuator to input states diagonal in the Fock basis coincides with the
thinning, the analogue of the rescaling for positive integer random variables.
Quantum Gaussian channels provide then a bridge between functional analysis and
discrete probability.
Description
Gaussian optimizers for entropic inequalities in quantum information
%0 Journal Article
%1 depalma2018gaussian
%A De Palma, Giacomo
%A Trevisan, Dario
%A Giovannetti, Vittorio
%A Ambrosio, Luigi
%D 2018
%K entropy-inequalities quantum
%T Gaussian optimizers for entropic inequalities in quantum information
%U http://arxiv.org/abs/1803.02360
%X We survey the state of the art for the proof of the quantum Gaussian
optimizer conjectures of quantum information theory. These fundamental
conjectures state that quantum Gaussian input states are the solution to
several optimization problems involving quantum Gaussian channels. These
problems are the quantum counterpart of three fundamental results of functional
analysis and probability: the Entropy Power Inequality, the sharp Young's
inequality for convolutions and the theorem "Gaussian kernels have only
Gaussian maximizers". Quantum Gaussian channels play a key role in quantum
communication theory: they are the quantum counterpart of Gaussian integral
kernels and provide the mathematical model for the propagation of
electromagnetic waves in the quantum regime. The quantum Gaussian optimizer
conjectures are needed to determine the maximum communication rates over
optical fibers and free space. The restriction of the quantum-limited Gaussian
attenuator to input states diagonal in the Fock basis coincides with the
thinning, the analogue of the rescaling for positive integer random variables.
Quantum Gaussian channels provide then a bridge between functional analysis and
discrete probability.
@article{depalma2018gaussian,
abstract = {We survey the state of the art for the proof of the quantum Gaussian
optimizer conjectures of quantum information theory. These fundamental
conjectures state that quantum Gaussian input states are the solution to
several optimization problems involving quantum Gaussian channels. These
problems are the quantum counterpart of three fundamental results of functional
analysis and probability: the Entropy Power Inequality, the sharp Young's
inequality for convolutions and the theorem "Gaussian kernels have only
Gaussian maximizers". Quantum Gaussian channels play a key role in quantum
communication theory: they are the quantum counterpart of Gaussian integral
kernels and provide the mathematical model for the propagation of
electromagnetic waves in the quantum regime. The quantum Gaussian optimizer
conjectures are needed to determine the maximum communication rates over
optical fibers and free space. The restriction of the quantum-limited Gaussian
attenuator to input states diagonal in the Fock basis coincides with the
thinning, the analogue of the rescaling for positive integer random variables.
Quantum Gaussian channels provide then a bridge between functional analysis and
discrete probability.},
added-at = {2018-03-09T15:14:00.000+0100},
author = {De Palma, Giacomo and Trevisan, Dario and Giovannetti, Vittorio and Ambrosio, Luigi},
biburl = {https://www.bibsonomy.org/bibtex/2e6c62e2a77601cc9adbc68390fb554e7/claired},
description = {Gaussian optimizers for entropic inequalities in quantum information},
interhash = {f87efad2b06279c6b033994f4e1bd0c4},
intrahash = {e6c62e2a77601cc9adbc68390fb554e7},
keywords = {entropy-inequalities quantum},
note = {cite arxiv:1803.02360},
timestamp = {2018-03-09T15:14:00.000+0100},
title = {Gaussian optimizers for entropic inequalities in quantum information},
url = {http://arxiv.org/abs/1803.02360},
year = 2018
}