夹层Rényi发散满足数据处理不等式
Sandwiched Rényi Divergence Satisfies Data Processing Inequality
摘要：
三明治（量子）$α$ -Rényi发散最近在Wilde等人（arXiv：1306.1586）和Müller-Lennert等人（arXiv：1306.3142v1）的独立工作中被定义。这种新的量子发散已经在量子信息理论中得到应用。在这里，我们进一步研究这种新量子发散的性质。特别是，我们表明，三明治$α$ -雷尼分歧满足数据处理不等式的所有值的$α> 1$。此外，我们还证明了由夹心$α$ -Rényi散度定义的Holevo信息的一种变体$α$ -Holevo信息是超可加的.我们的结果是基于Hölder不等式，Riesz-Thorin定理和复插值理论的思想。我们还采用Sion的极大极小定理。
英文摘要：
Sandwiched (quantum) $α$-Rényi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and Müller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications in quantum information theory. Here we further investigate properties of this new quantum divergence. In particular we show that sandwiched $α$-Rényi divergence satisfies the data processing inequality for all values of $α> 1$. Moreover we prove that $α$-Holevo information, a variant of Holevo information defined in terms of sandwiched $α$-Rényi divergence, is super-additive. Our results are based on Hölder's inequality, the Riesz-Thorin theorem and ideas from the theory of complex interpolation. We also employ Sion's minimax theorem.
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