相对熵联合凸性的又一证明
量子物理
2022-09-07 v3 信息论
数学物理
泛函分析
math.IT
math.MP
摘要
利用映射 的联合凸性、算子凸函数的积分表示以及 Ando 的一个观察，我们得到了相对熵联合凸性与 Lieb 的一个迹凸性结果的简单证明。后者是量子熵强次可加性原始证明中的关键要素。
引用
@article{arxiv.2112.13763,
title = {Yet Another Proof of the Joint Convexity of Relative Entropy},
author = {Mary Beth Ruskai},
journal= {arXiv preprint arXiv:2112.13763},
year = {2022}
}
备注
Added dedication to Derek W. Robinson. Added proof of the montonicity of relative entropy under partial traces and strong subadditivity of quantum entropy to v2. Added to v3, a section on generalizations of relative entropy and a remark (not in LMP version) proving the joint convexity of relative entropy using an integral representation for log x instead of operator convex functions