论文标题
纠缠边缘问题
Entanglement marginal problems
论文作者
论文摘要
我们考虑纠缠边缘问题，该问题包括确定许多降低的密度矩阵是否与总体可分离量子状态兼容。为了解决这个问题，我们提出了一组量子状态边缘的半决赛编程放松的层次结构，承认完全可分离的扩展。我们将每个层次结构的完整性与模拟经典边缘问题的解决方案联系起来，从而确定层次结构完成的相关实验情况。对于有限的恒星配置或链条上的许多各方，我们发现我们可以在系统尺寸上使用时间（空间）复杂性多项式（线性）来实现与可分离状态的最接近的邻居边缘的近似值。我们的结果甚至扩展到无限系统，例如1D中的翻译不变系统，以及具有额外对称性的较高空间维度。
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.
