Quantum relative entropy: general convergence criterion and preservation of convergence under completely positive linear maps

Abstract

A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum relative entropy under completely positive linear maps is established.

arXiv comment33 pages, any comments are welcome

References in corpus (7)

• The Role of Relative Entropy in Quantum Information Theory
• Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
• Entropic characteristics of subsets of states
• Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
• On quantum channels and operations preserving finiteness of the von Neumann entropy
• Convergence conditions for the quantum relative entropy and other applications of the deneralized quantum Dini lemma
• Strong* convergence of quantum channels

Cited by in corpus (2)

• Continuity bounds for quantum entropies arising from a fundamental entropic inequality
• Zero-error communication under discrete-time Markovian dynamics