A limit relation for entropy and channel capacity per unit cost

Abstract

In a quantum mechanical model, Diosi, Feldmann and Kosloff arrived at a conjecture stating that the limit of the entropy of certain mixtures is the relative entropy as system size goes to infinity. The conjecture is proven in this paper for density matrices. The first proof is analytic and uses the quantum law of large numbers. The second one clarifies the relation to channel capacity per unit cost for classical-quantum channels. Both proofs lead to generalization of the conjecture.

LATEX file, 11 pages

References in corpus (2)

• Coding Theorems for Quantum Channels
• A quantum version of Sanov's theorem

Cited by in corpus (6)

• Quantum message compression with applications
• Optimal quantum channels
• Quantum Channel Capacities Per Unit Cost
• Bounding the resources for thermalizing many-body localized systems
• Operational meaning of the classical fidelity and the path length in Fisher-Kubo-Mori-Bogoliubov geometry
• On the limit relation for the quantum relative entropy