论文标题
量子资源理论中鲁棒性措施的连续性
Continuity of robustness measures in quantum resource theories
论文作者
论文摘要
鲁棒性措施是越来越重要的资源量化符，这些量子已被引入量子资源理论，例如纠缠和连贯性。尽管这些措施的普遍性，但它们的某些数学属性仍然不清楚，尤其是当一组无资源的状态是非convex时，它们的有用性仍受到阻碍。在本文中，我们研究了不同鲁棒性函数的连续性。我们表明它们的连续性取决于自由状态集的形状。特别是，我们证明，在许多情况下，恒星凸度足以满足鲁棒性的Lipschitz-continention，并且我们提供了导致非连续措施的集合的特定示例。最后，我们通过定义可遗传性和量子不一调的鲁棒性来说明结果的适用性。
Robustness measures are increasingly prominent resource quantifiers that have been introduced for quantum resource theories such as entanglement and coherence. Despite the generality of these measures, their usefulness is hindered by the fact that some of their mathematical properties remain unclear, especially when the set of resource-free states is non-convex. In this paper, we investigate continuity properties of different robustness functions. We show that their continuity depends on the shape of the set of free states. In particular, we demonstrate that in many cases, star-convexity is sufficient for Lipschitz-continuity of the robustness, and we provide specific examples of sets leading to non-continuous measures. Finally, we illustrate the applicability of our results by defining a robustness of teleportability and of quantum discord.
