Non-commutative Nash inequalities

DOI10.1063/1.4937382zbMath1330.81058arXiv1508.02522OpenAlexW3099327563MaRDI QIDQ2786622

Kristan Temme, Michael J. Kastoryano

Publication date: 15 February 2016

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

Full work available at URL: https://arxiv.org/abs/1508.02522

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Ergodicity, mixing, rates of mixing (37A25) Linear operators defined by compactness properties (47B07) Quantum stochastic calculus (81S25) Measures of information, entropy (94A17) Channel models (including quantum) in information and communication theory (94A40) Coding theorems (Shannon theory) (94A24) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (4)

A nonlocal transform to map and track quantum dynamics ⋮ Contractivity properties of a quantum diffusion semigroup ⋮ Fisher information and logarithmic Sobolev inequality for matrix-valued functions ⋮ Concentration of quantum states from quantum functional and transportation cost inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Thermalization time bounds for Pauli stabilizer Hamiltonians
• Nash inequalities for finite Markov chains
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Hardy-Littlewood theory for semigroups
• Upper bounds for symmetric Markov transition functions
• Stability of local quantum dissipative systems
• Hypercontractivity for semigroups of unital qubit channels
• Hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup
• Quantum Gibbs samplers: the commuting case
• Hypercontractivity of quasi-free quantum semigroups
• Quantum Subdivision Capacities and Continuous-Time Quantum Coding
• A cutoff phenomenon for quantum Markov chains
• Logarithmic Sobolev Inequalities
• Minimal entropy of states emerging from noisy quantum channels
• Additivity for unital qubit channels
• The $\chi ^2$χ2-divergence and mixing times of quantum Markov processes
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Rapid mixing implies exponential decay of correlations
• Sandwiched Rényi divergence satisfies data processing inequality

This page was built for publication: Non-commutative Nash inequalities