论文标题
反驳量子边缘的光谱兼容性
Refuting spectral compatibility of quantum marginals
论文作者
论文摘要
量子边缘问题的频谱变体要问：一组重叠量子边缘的规定光谱，是否存在兼容的关节状态？这项工作的主要思想是一种对称性的半决赛编程层次结构，该层次结构检测到何时不存在这种联合状态。从某种意义上说，层次结构是完整的，它检测到每一套不兼容的光谱集。它提供的反驳是无维度的，在所有本地维度上都证明了不相容性。该层次结构还适用于Hermitian矩阵问题的总和，局部单一不变性的兼容性，用于证明消失的Kronecker系数，并优化在epovariast的状态多项式方面。
The spectral variant of the quantum marginal problem asks: Given prescribed spectra for a set of overlapping quantum marginals, does there exist a compatible joint state? The main idea of this work is a symmetry-reduced semidefinite programming hierarchy that detects when when no such joint state exists. The hierarchy is complete, in the sense that it detects every incompatible set of spectra. The refutations it provides are dimension-free, certifying incompatibility in all local dimensions. The hierarchy also applies to the sums of Hermitian matrices problem, the compatibility of local unitary invariants, for certifying vanishing Kronecker coefficients, and to optimize over equivariant state polynomials.
