并行量子信道鉴别与张量积子空间中的数值域
Parallel quantum channel discrimination and numerical ranges in tensor product subspaces
- VSB–Technical University of Ostrava（俄斯特拉发科技大学）
- IT4Innovations, VSB–Technical University of Ostrava（俄斯特拉发科技大学 IT4创新研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究针对并行量子信道完美鉴别问题，提出结合半定规划与二分法的高效算法，并证明张量积子空间数值域最小角度的可加性，从而肯定解决了一个公开猜想。
AI中文摘要：
量子信道鉴别在量子信息理论中扮演着至关重要的角色。特别令人感兴趣的是信道可以被完美鉴别的情形。在本工作中，我们关注并行方案下的完美量子信道鉴别任务。我们开发了一种结合二分过程的半定规划（SDP）公式，用于计算一个量子态，以实现与副本数量成线性时间的完美鉴别。此外，我们获得了实现完美鉴别所需的量子信道的最小副本数量。借此，我们肯定地解决了Duan、Guo、Li和Li [arXiv:1605.02294, IEEE ISIT 2016]中的猜想1，该猜想刻画了完美鉴别一个特殊算子子空间族所需的并行使用次数。我们所有的结果都是利用数值域的概念和基本性质获得的。特别地，我们证明并使用的关键事实是：矩阵子空间张量积的数值域的最小角度等于各个子空间数值域的最小角度之和。
英文摘要：
Quantum channel discrimination plays a crucial role in quantum information theory. Of particular interest is the case in which the channels can be discriminated perfectly. In this work, we focus on the perfect quantum channel discrimination task in a parallel scheme. We develop an SDP formulation combined with a bisection procedure to compute a quantum state for perfect discrimination in time linear in the number of copies. In addition, we obtain the minimal number of copies of quantum channels to achieve perfect discrimination. Thanks to that, we settle in the affirmative Conjecture 1 of Duan, Guo, Li and Li [arXiv:1605.02294, IEEE ISIT 2016], which characterizes the number of parallel uses needed to discriminate perfectly a distinguished family of operator subspaces. All our results are obtained using the notion and basic properties of the numerical range. In particular, the key fact that we prove and use is that the minimal angle of the numerical range of a tensor product of matrix subspaces equals the sum of the minimal angles of the numerical ranges of the individual subspaces.
