无凸性限制的基于鲁棒性和权重的资源度量：静态与动态量子资源理论中的多拷贝见证与操作优势
Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
AI总结：
本文通过引入非线性多拷贝见证和信道区分/排除任务的操作解释，在无凸性限制的一般量子资源理论中表征了广义鲁棒性和资源权重，证明了这些度量在传统凸QRTs范围之外的有效性。
摘要：
量子资源理论（QRTs）提供了一个统一的框架，用于分析量子属性作为资源在量子信息处理中实现优势。广义鲁棒性和资源权重作为有用的资源量化指标，正受到越来越多的关注。然而，对这些度量的现有分析仅限于假设自由状态集合满足凸性的情况，而物理上具有启发性的资源并不一定满足这一限制。在本文中，我们通过两种不同但相关的方法，对无凸性限制的一般QRTs中基于鲁棒性和权重的度量进行了表征。一方面，我们通过引入非线性见证来表征广义鲁棒性和资源权重。我们展示了新的见证可观测量的通用构造，这些可观测值从状态的多个拷贝中检测给定状态的资源性，并且使用这些见证，即使在没有任何凸性假设的情况下，我们也为上述资源度量提供了操作解释。另一方面，我们发现广义鲁棒性和资源权重也可以分别被解释为信道区分和信道排除任务变体中的最坏情况最大优势，其中自由状态集合由对应于多重限制的多个凸子集组成。我们进一步将这些结果扩展到量子信道和量子仪的QRTs中。这些表征表明，即使在无凸性假设的一般QRTs中，每种量子资源在相应任务中均展现出优势。因此，我们确立了基于鲁棒性和权重的技术在传统凸QRTs范围之外的有效性，从而促进了对QRTs一般结构的更好理解。
英文摘要：
Quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining increasing attention as useful resource quantifiers. However, the existing analyses of these measures were restricted to the cases where convexity of the set of free states is assumed, and physically motivated resources do not necessarily satisfy this restriction. In this paper, we give characterizations of robustness- and weight-based measures in general QRTs without convexity restriction through two different yet related approaches. On the one hand, we characterize the generalized robustness and the weight of resource by introducing a nonlinear witness. We show a general construction of new witness observables that detect the resourcefulness of a given state from multiple copies of the state and, using these witnesses, we provide operational interpretations of the above resource measures even without any convexity assumption. On the other hand, we find that the generalized robustness and the weight of resource can also be interpreted as the worst-case maximum advantage in variants of channel-discrimination and channel-exclusion tasks, respectively, where the set of free states consists of several convex subsets corresponding to multiple restrictions. We further extend these results to QRTs for quantum channels and quantum instruments. These characterizations show that every quantum resource exhibits an advantage for the corresponding tasks, even in general QRTs without convexity assumption. Thus, we establish the usefulness of robustness-based and weight-based techniques beyond the conventional scope of convex QRTs, leading to a better understanding of the general structure of QRTs.
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