Coding Theorems for Compound Problems via Quantum Rényi Divergences

PROJECT TITLE :

Coding Theorems for Compound Problems via Quantum Rényi Divergences

ABSTRACT:

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 variety of applications in robust converse theorems. Here, we have a tendency to show that these new Rényi divergences are helpful tools to obtain coding theorems in the direct domain of numerous problems. We have a tendency to demonstrate this by giving new and significantly simplified proofs for the achievability elements of Stein’s lemma with composite null-hypothesis, universal state compression, and also the classical capacity of compound classical-quantum channels, based on single-shot error bounds already obtainable within the literature and easy 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 straightforward null-hypothesis/single source/single channel.

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