近日，孟买印度理工学院的Arindam Mitra及其研究团队取得一项新进展。经过不懈努力，他们揭示动态映射的完全正可分性与通道兼容性的关系。相关研究成果已于2024年6月13日在国际知名学术期刊《物理评论A》上发表。

本研究深入探讨了CP可分性与通道相容性之间错综复杂的关联。研究人员专注于一类通用动态映射的量子信道，并分析了其不兼容鲁棒性的行为。他们成功证明，对于这类通用的CP可分动态映射，其信道的不相容鲁棒性呈现出单调非递增的特性。

更进一步，研究人员对特定动态映射的不相容鲁棒性随时间的变化进行了详细的研究，揭示了CP不可分区域中的非单调性现象。此外，他们还提出一种基于量子信道不相容鲁棒性的CP不可分性度量方法。这项研究为量子动力学映射的本质及其在信息理论应用中的相关性提供了有价值的见解。

据悉，完全正不可分性(CP不可分性)和不相容性作为各种信息论任务的宝贵资源，其作用已得到广泛认可。

附：英文原文

Title: Relating completely positive divisibility of dynamical maps with compatibility of channels

Author: Arindam Mitra, Debashis Saha, Samyadeb Bhattacharya, A. S. Majumdar

Issue&Volume: 2024/06/13

Abstract: The role of completely positive–indivisibility (CP-indivisibility) and incompatibility as valuable resources for various information-theoretic tasks is widely acknowledged. This study delves into the intricate relationship between CP-divisibility and channel compatibility. Our investigation focuses on the behavior of incompatibility robustness of quantum channels for a pair of generic dynamical maps. We show that the incompatibility robustness of channels is monotonically nonincreasing for a pair of generic CP-divisible dynamical maps. Further, our explicit study of the behavior of incompatibility robustness with time for some specific dynamical maps reveals nonmonotonic behavior in the CP-indivisible regime. Additionally, we propose a measure of CP-indivisibility based on the incompatibility robustness of quantum channels. Our investigation provides valuable insights into the nature of quantum dynamical maps and their relevance in information-theoretic applications.

DOI: 10.1103/PhysRevA.109.062213

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.062213