论文标题
绝对$ k $ - 赋予量子状态和光谱不平等的矩阵因子宽度
Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix
论文作者
论文摘要
我们研究了仅基于其特征值的$ k $ incerent的一组量子状态（等效地，我们探索哪些遗传矩阵只能证明只有基于其特征值的小因子宽度）。类似于量子资源理论中的绝对可分离性问题，我们称这些状态为“绝对$ k $ inccorent”，并且在此集合中为会员资格提供了几个必要和足够的条件。我们通过利用有关与基本对称多项式相关的双曲线锥的最新结果来获得许多结果。
We investigate the set of quantum states that can be shown to be $k$-incoherent based only on their eigenvalues (equivalently, we explore which Hermitian matrices can be shown to have small factor width based only on their eigenvalues). In analogy with the absolute separability problem in quantum resource theory, we call these states "absolutely $k$-incoherent", and we derive several necessary and sufficient conditions for membership in this set. We obtain many of our results by making use of recent results concerning hyperbolicity cones associated with elementary symmetric polynomials.
