论文标题
线性系统的完整层次结构，用于证明子空间的量子纠缠
A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
论文作者
论文摘要
我们引入了线性系统的层次结构，以表明给定的纯量子状态的子空间是纠缠的（即，不包含产品状态）。该层次结构在第一层已经超过了已知的方法，并且从某种意义上说，每个纠缠的子空间都显示在层次结构的某些有限级别上。它直接概括为较高的Schmidt等级，以及完全纠缠的子空间的多部分情况。这些层次结构在实践中即使在非常大的量子系统中也非常有效，因为它们可以通过基本线性代数技术实现，而不是先前已知的层次结构所要求的半决赛编程技术。
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in the sense that every entangled subspace is shown to be so at some finite level of the hierarchy. It generalizes straightforwardly to the case of higher Schmidt rank, as well as the multipartite cases of completely and genuinely entangled subspaces. These hierarchies work extremely well in practice even in very large quantum systems, as they can be implemented via elementary linear algebra techniques rather than the semidefinite programming techniques that are required by previously-known hierarchies.
