Contraction coefficients for noisy quantum channels

Abstract

Generalized relative entropy, monotone Riemannian metrics, geodesic distance, and trace distance are all known to decrease under the action of quantum channels. We give some new bounds on, and relationships between, the maximal contraction for these quantities.

40 pages

References in corpus (3)

• Quantum logarithmic Sobolev inequalities and rapid mixing
• Trace functions as Laplace transforms
• Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

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• Quantum Brascamp-Lieb Dualities
• Limits of noisy quantum metrology with restricted quantum controls
• Emergence of noise-induced barren plateaus in arbitrary layered noise models
• Jointly constrained semidefinite bilinear programming with an application to Dobrushin curves
• Tensorization of the strong data processing inequality for quantum chi-square divergences
• Quantum Local Differential Privacy and Quantum Statistical Query Model
• Yet Another Proof of the Joint Convexity of Relative Entropy
• Maximal trace distance between isoenergetic bosonic Gaussian states
• Reverse-type Data Processing Inequality
• Zero-error communication under discrete-time Markovian dynamics
• Information storage and transmission under Markovian noise