论文标题
对称状态的量子边缘问题：用于变分优化，非局部性和自我测试的应用
The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
论文作者
论文摘要
在本文中，我们提出了一种解决对称$ d $级别系统的量子边缘问题的方法。该方法建立在一个有效的半明确程序的基础上，该程序确定了$ m $体体降低密度的兼容性条件，并在对称空间上支持的全局$ n $ body密度矩阵。我们说明了该方法在中央量子信息问题中的适用性，其中有几个示例性的案例研究。即，（i）快速变异的ANSATZ，以优化当地的哈密顿量超过对称状态，（ii）一种优化对称的，几个体钟算子而不是对称状态的方法，以及（iii）一组足够的条件来确定哪些对称状态不能从几乎没有物体观察物中进行自我测试。作为我们发现的副产品，我们还提供了$ n $ qubit dicke States的任意叠加与翻译不变的对角线矩阵产品债券尺寸$ n $之间的通用分析对应关系。
In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced density with a global $n$-body density matrix supported on the symmetric space. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies. Namely, (i) a fast variational ansatz to optimize local Hamiltonians over symmetric states, (ii) a method to optimize symmetric, few-body Bell operators over symmetric states and (iii) a set of sufficient conditions to determine which symmetric states cannot be self-tested from few-body observables. As a by-product of our findings, we also provide a generic, analytical correspondence between arbitrary superpositions of $n$-qubit Dicke states and translationally-invariant diagonal matrix product states of bond dimension $n$.
