论文标题
用于通用爱因斯坦 - 波多尔斯基 - 罗森场景的半决赛计划的层次结构
A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
论文作者
论文摘要
爱因斯坦 - 波多尔斯基 - 罗森（EPR）场景中的相关性，由\ textit {complages}捕获的非正态量化状态，最近从基础和信息理论的角度引起了社区的关注。一组可实现的组合或缩写为量子组合，是由多个在共享量子系统上执行本地测量的各方引起的。通常，确定给定的组合是否是量子组合，即量子组合集的成员资格是一个困难的问题，并且并非总是可以解决的。在本文中，我们介绍了测试的层次结构，其中每个级别要么确定一组量子组合的非成员，要么尚无定论。层次结构的级别越高，可以确定非会员的级别，并且该层次结构会收敛到一组特定的组合。此外，它收敛到的集合包含量子组合。层次结构中的每个测试均以半决赛计划进行配合。该层次结构允许在通信或信息处理任务中量子EPR组合提供的量子违反转向不等式的量子违反量子。
Correlations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by \textit{assemblages} of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. The set of quantum-realisable assemblages, or abbreviated to quantum assemblages, are those that arise from multiple parties performing local measurements on a shared quantum system. In general, deciding whether or not a given assemblage is a quantum assemblage, i.e. membership of the set of quantum assemblages, is a hard problem, and not always solvable. In this paper we introduce a hierarchy of tests where each level either determines non-membership of the set of quantum assemblages or is inconclusive. The higher the level of the hierarchy the better one can determine non-membership, and this hierarchy converges to a particular set of assemblages. Furthermore, this set to which it converges contains the quantum assemblages. Each test in the hierarchy is formulated as a semidefinite program. This hierarchy allows one to upper bound the quantum violation of a steering inequality and the quantum advantage provided by quantum EPR assemblages in a communication or information-processing task.
