Instrument-based quantum resources: quantification, hierarchies and towards constructing resource theories
中文速览 本文系统地构建了一套针对量子仪器（quantum instrument）的量子资源理论框架。量子仪器是描述量子测量过程的通用数学工具，它不仅给出测量的经典结果，还描述了测量后量子态的演化，因此在多方或序贯量子任务中至关重要。尽管基于量子态和测量的资源理论已得到充分研究，但基于仪器的理论仍是片空白。该论文填补了这一空白，首次为多种以仪器为载体的资源（如信息保持能力、纠缠保持能力、不相容性保持能力等）建立了严格的资源理论。作者们明确了各类资源理论中的“自由对象”与“自由操作”，建立并证明了不同仪器资源之间的层级关系，并提出了一种基于金刚石范数（diamond norm）的通用量化方法。这项工作为理解、量化和利用在复杂量子协议中至关重要的操作性资源提供了坚实的理论基础。 English Research Briefing Research Briefing: Instrument-based quantum resources: quantification, hierarchies and towards constructing resource theories 1. The Core Contribution This paper establishes a comprehensive and unified framework for constructing multiple quantum resource theories based on quantum instruments. While resource theories for static objects like quantum states or simple operations like measurements are well-established, this work extends the paradigm to quantum instruments—the general mathematical objects describing measurement—which simultaneously provide classical outcomes and post-measurement quantum states. The central contribution is the systematic development of five distinct instrument-based resource theories (information, entanglement, and incompatibility preservability, alongside traditional and parallel incompatibility), where for each theory, the authors define the set of free objects and derive the corresponding set of free physical transformations. Crucially, they introduce a robust, distance-based quantification method and prove its validity across all these theories, while also establishing a clear hierarchy among these operational resources, demonstrating, for example, that entanglement preservability is a strictly stronger resource than incompatibility preservability. ...