2007/04/30 by Motohisa Fukuda, Michael M. Wolf
Computer Science · Engineering · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wireless Communication Security Techniques #quant-ph
paper · pdf · doi:10.1063/1.2746128
published as J. Math. Phys. 48, 072101 (2007) · 5 pages
openalex publication_date 2007/07/01 · arxiv created 2007/08/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy, and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds if and only if it holds for arbitrary equal pairs, which in turn can be taken to be unital. In a similar sense, weak additivity is shown to imply strong additivity for any convex entanglement monotone. The implications are obtained by considering direct sums of channels (or states) for which we show how to obtain several information theoretic quantities from their values on the summands. This provides a simple and general tool for lifting additivity results.