## Quantum Rényi Divergence Satisfies Data Processing Inequality    [PDF]

Salman Beigi
Quantum $\alpha$-R\'enyi divergence has been recently defined by Wilde et al. (arXiv:1306.1586) and M\"uller-Lennert et al (arXiv:1306.3142). In the former paper this new divergence is called "sandwiched" R\'enyi relative entropy and is used to prove a strong converse for classical capacity of entanglement-breaking channels. The latter paper studies some properties of quantum R\'enyi divergence and contains several conjectures. Here we further investigate properties of this new quantum divergence and prove all of these conjectures when $\alpha>1$. In particular we show that quantum $\alpha$-R\'enyi divergence satisfies the data processing inequality for all values of $\alpha> 1$.
View original: http://arxiv.org/abs/1306.5920