Quantum Entropy Contraction and Factorization from Hypercontractivity

arXiv:2609.20753 · quant-ph, math.FA, math.OA · Submitted 2026-09-17 · Read on arXiv

quant-ph, math.FA, math.OA

Submitted: 2026-09-17

Updated: 2026-10-05

Comments: 15 pages; comments are welcome

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 7× in this paper · explained in 2 episodes
• Spectral Gap — 6× in this paper · explained in 5 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes

Sources

• Estimating the decoherence time using non-commutative Functional Inequalities
• Sandwiched R'enyi Divergence Satisfies Data Processing Inequality
• Quantum reverse hypercontractivity: its tensorization and application to strong converses
• Entropy Contractions in Markov Chains: Half-Step, Full-Step and Continuous-Time
• Stability of logarithmic Sobolev inequalities under a noncommutative change of measure
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Entropy Production of Doubly Stochastic Quantum Channels
• Convergence Rates of Two-Component MCMC Samplers
• A noncommutative martingale convexity inequality
• Hyper-contractivity and entropy decay in discrete time
• Hypercontractivity of quasi-free quantum semigroups
• The metric property of the quantum Jensen-Shannon divergence
• $L_{p}$-improving convolution operators on finite quantum groups

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