5 citations · 12 across the 7 of their papers we have counts for
11 papers
Complete Modified Logarithmic Sobolev inequality for sub-Laplacian on
Li Gao, Maria Gordina
We prove that the canonical sub-Laplacian on admits a uniform modified log-Sobolev inequality for all its matrix-valued functions, independent of the matrix dimension. This…
Strong Converse for Privacy Amplification against Quantum Side Information
Yu-Chen Shen, Li Gao, Hao-Chung Cheng
We establish a one-shot strong converse bound for privacy amplification against quantum side information using trace distance as a security criterion. This strong converse bound im…
Ricci curvature of quantum channels on non-commutative transportation metric spaces
Li Gao, Cambyse Rouzé
Following Ollivier's work, we introduce the coarse Ricci curvature of a quantum channel as the contraction of non-commutative metrics on the state space. These metrics are defined…
Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
Li Gao, Marius Junge, Haojian Li
In this paper, we use the Carnot-Caratheodory distance from sub-Riemanian geometry to prove entropy decay estimates for all finite dimensional symmetric quantum Markov semigroups.…
Complete Logarithmic Sobolev Inequalities via Ricci Curvature Bounded Below II
Michael Brannan, Li Gao, Marius Junge
Using a non-negative curvature condition, we prove the complete version of modified log-Sobolev inequalities for central Markov semigroups on various compact quantum groups, includ…
Complete Logarithmic Sobolev inequalities via Ricci curvature bounded below
Michael Brannan, Li Gao, Marius Junge
We prove that for a symmetric Markov semigroup, Ricci curvature bounded from below by a non-positive constant combined with a finite -mixing time implies the modified log…