基于方向迭代的最小误差量子测量、量子动力学可逆性及最大重叠问题的双边界
摘要
在一个统一框架下，我们获得了量子信息理论中以下感兴趣量的双边估计：1. 任意混合量子态系综的最小误差可区分性。2. 以纠缠保真度度量的量子动力学的近似可逆性（当反向信道是编码操作与噪声信道的复合时，这也被称为“信道适配的量子错误恢复”）。3. 通过对混合态的一部分施加局域量子操作，二分纯量子态与二分混合态之间可实现的最大重叠。4. 二分量子态的条件最小熵。采用作者用于界定第一个量的技术的改进版本[J. Math. Phys. 50, 032016]，对剩余三个量给出了双边估计。我们的主要工具是“小角度”初始化，这是对Jezek-Rehacek-Fiurasek [Phys. Rev. A 65, 060301]、Jezek-Fiurasek-Hradil [Phys. Rev. A 68, 012305]和Reimpell-Werner [Phys. Rev. Lett 94, 080501]引入的用于计算最优测量和量子错误恢复的迭代方案的抽象推广。
引用
@article{arxiv.0907.3386,
title = {Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates},
author = {Jon Tyson},
journal= {arXiv preprint arXiv:0907.3386},
year = {2010}
}
备注
Extensively revised & new content added. Improved min-entropy bounds. Notation made more accessible. Minimax theorem used to clarify relationship between "worst case" bounds and "single instance" bounds. Improved motivation of the choice of "small angle" guess. Eliminated spurious factor appearing when overlap bounds are applied to state distinction. Work connected to that of Beny and Oreshkov