联合数值域和量子态的Kippenhahn定理
Kippenhahn's Theorem for joint numerical ranges and quantum states
摘要：
Kippenhahn定理断言矩阵的数值域是某一代数曲线的凸包。在这里，我们证明了许多埃尔米特矩阵的联合数值域类似于半代数集的凸包。本文讨论了对偶凸锥与双曲锥的一个类似的命题，并证明了这类对偶锥的基类在线性运算下是闭的。这一结果为分析量子态提供了一种新的几何方法。
英文摘要：
Kippenhahn's Theorem asserts that the numerical range of a matrix is the convex hull of a certain algebraic curve. Here, we show that the joint numerical range of finitely many Hermitian matrices is similarly the convex hull of a semi-algebraic set. We discuss an analogous statement regarding the dual convex cone to a hyperbolicity cone and prove that the class of bases of these dual cones is closed under linear operations. The result offers a new geometric method to analyze quantum states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
