论文标题
通过分布的相对熵
Relative Entropy via Distribution of Observables
论文作者
论文摘要
我们从阳性自偏操作员的分布概念中获得了Petz-Rényi和Umegaki相对熵的公式。对Rényi和Kullback-Leibler差异的经典结果用于获得有关Petz-Rényi和Umegaki相对熵的一些已知结果的新结果和新证明。其中最重要的是，对于Petz-rényi$α$偏向熵的有限性，必要且充分的条件。此处介绍的所有结果在有限和无限维度上都是有效的。特别是，这些结果适用于Fock空间中的状态，因此适用于连续可变量子信息理论。
We obtain formulas for Petz-Rényi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on Rényi and Kullback-Leibler divergences are applied to obtain new results and new proofs for some known results about Petz-Rényi and Umegaki relative entropy. Most important among these, is a necessary and sufficient condition for the finiteness of the Petz-Rényi $α$-relative entropy. All of the results presented here are valid in both finite and infinite dimensions. In particular, these results are valid for states in Fock spaces and thus are applicable to continuous variable quantum information theory.
