2013/10/31 by Milán Mosonyi, Milan Mosonyi · 25 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Coding (social sciences) #Coding theory #Converse #Lemma (botany) #Mathematical proof #Novelty #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Simple (philosophy) #Wireless Communication Security Techniques #cs.IT #math-ph #math.IT #math.MP #quant-ph
paper · pdf · doi:10.1109/tit.2015.2417877
published in IEEE Transactions on Information Theory 61(6), 2997-3012 (Institute of Electrical and Electronics Engineers) · v4: 16 pages, accepted for publication in IEEE Transactions on Information Theory
openalex publication_date 2015/04/14 · arxiv created 2016/06/23 · arxiv updated 2016/06/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recently, a new notion of quantum Rényi divergences has been introduced by Müller-Lennert, Dupuis, Szehr, Fehr, and Tomamichel and Wilde, Winter, and Yang, which found a number of applications in strong converse theorems. Here, we show that these new Rényi divergences are also useful tools to obtain coding theorems in the direct domain of various problems. We demonstrate this by giving new and considerably simplified proofs for the achievability parts of Stein's lemma with composite null-hypothesis, universal state compression, and the classical capacity of compound classical-quantum channels, based on single-shot error bounds already available in the literature and simple properties of the quantum Rényi divergences. The novelty of our proofs is that the composite/compound coding theorems can be almost directly obtained from the single-shot error bounds, essentially with the same effort as for the case of simple null-hypothesis/single source/single channel.