动力学映射的 CP 可分性与信道相容性之间的关联
Relating CP divisibility of dynamical maps with compatibility of channels
AI总结：
本文研究动力学映射 CP 可分性与信道相容性的关系，证明 CP 可分映射下不相容鲁棒性单调非增，并基于该鲁棒性提出 CP 不可分性度量。
AI中文摘要：
CP 不可分性与不相容性作为多种信息论任务中宝贵资源的作用已得到广泛认可。本研究深入探讨了 CP 可分性与量子信道相容性之间的复杂关系。我们的研究聚焦于一对一般动力学映射下量子信道不相容鲁棒性的行为。我们证明，对于一对一般的 CP 可分动力学映射，信道的不相容鲁棒性是单调非增的。此外，我们对若干特定动力学映射中不相容鲁棒性随时间变化行为的显式研究，揭示了其在 CP 不可分区域内的非单调行为。另外，我们基于量子信道的不相容鲁棒性提出了一种 CP 不可分性的度量。本研究为理解量子动力学映射的本质及其在信息论应用中的相关性提供了有价值的见解。
英文摘要：
The role of 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 behaviour of incompatibility robustness of quantum channels for a pair of generic dynamical maps. We show that the incompatibility robustness of channels is monotonically non-increasing for a pair of generic CP-divisible dynamical maps. Further, our explicit study of the behaviour of incompatibility robustness with time for some specific dynamical maps reveals non-monotonic behaviour 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.
