论文标题
两个量子双腹场景的两个收敛性NPA样层次结构
Two convergent NPA-like hierarchies for the quantum bilocal scenario
论文作者
论文摘要
表征由局部测量关节量子系统的一个部分引起的相关性是量子信息理论的主要问题之一。开创性的工作[M. Navascués等人，NJP 10,7,073013（2008）]（被称为NPA层次结构）将这个问题重新制定为非交通变量的多项式优化问题，并提出了必要条件的收敛层次结构，每种条件都可以使用半决赛编程进行测试。最近，表征量子网络相关性的问题是在本地测量网络中分布在网络中的几个独立量子系统时出现的问题。 NPA层次结构的几种概括，例如标量扩展[Pozas-Kerstjens等，Phys。莱特牧师。引入了123，140503（2019）]，而它们的融合集仍然未知。在这项工作中，我们介绍了一个新的层次结构，证明了它与标量扩展的等效性，并在最简单的网络，双尾场场景中表征了其收敛性，并探索了其与已知概括的关系。
Characterising the correlations that arise from locally measuring a single part of a joint quantum system is one of the main problems of quantum information theory. The seminal work [M. Navascués et al, NJP 10,7,073013 (2008)], known as the NPA hierarchy, reformulated this question as a polynomial optimisation problem over noncommutative variables and proposed a convergent hierarchy of necessary conditions, each testable using semidefinite programming. More recently, the problem of characterising the quantum network correlations, which arise when locally measuring several independent quantum systems distributed in a network, has received considerable interest. Several generalisations of the NPA hierarchy, such as the Scalar Extension [Pozas-Kerstjens et al, Phys. Rev. Lett. 123, 140503 (2019)], were introduced while their converging sets remain unknown. In this work, we introduce a new hierarchy, prove its equivalence to the Scalar Extension, and characterise its convergence in the case of the simplest network, the bilocal scenario, and explore its relations with the known generalisations.
