理解纠缠与非定域性的相互作用：推动并发展纠缠理论的一个新分支
Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
AI总结：
本文提出以局域操作与共享随机性（LOSR）替代LOCC作为自由操作，解决非定域性异常、建立无病态特征的多体纠缠与非定域性概念，并推广自检验的资源论解释，从而开创纠缠理论新分支。
摘要：
量化资源的一种标准方法是确定对资源的哪些操作是自由可用的，并推导出在自由操作下由可转换关系所诱导的资源偏序。如果所关注的资源是量子态中所体现关联的非经典性，即纠缠，那么通常的假设是自由操作的适当选择为局域操作与经典通信（LOCC）。本文主张研究一种不同的自由操作选择，即局域操作与共享随机性（LOSR），并展示其在理解贝尔实验中态的纠缠与关联的非定域性之间相互作用方面的效用。具体而言，我们表明LOSR范式（i）为非定域性的异常现象提供了一种解决方案，其中部分纠缠态比最大纠缠态表现出更多的非定域性；（ii）引入了真正的多体纠缠和非定域性的新概念，这些概念摆脱了传统概念中的病态特征；（iii）使得对纠缠态自检验的资源论解释成为可能，该解释推广并简化了先前的结果。在此过程中，我们推导了一些关于纯纠缠态在LOSR下可转换性的充要条件的基本结果，并强调了它们的一些推论，例如两体纯态催化不可能性。资源论视角还阐明了为什么存在不违反任何贝尔不等式的混合纠缠态既不令人惊讶也不成问题。我们的结果推动了对LOSR纠缠作为纠缠理论新分支的研究。
英文摘要：
A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., entanglement, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
