联合数值范围和量子态的Kippenhahn定理

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2019-07-10 DOI:10.1137/19M1286578

D. Plaumann, Rainer Sinn, S. Weis

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引用次数: 9

摘要

Kippenhahn定理断言矩阵的数值范围是某代数曲线的凸包。在这里，我们证明了有限多个厄米矩阵的联合数值范围类似于半代数集的凸包。讨论了对偶凸锥与双曲锥的一个类似命题，并证明了对偶凸锥的凸基类在线性运算下是闭的。该结果为量子态分析提供了一种新的几何方法。

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Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States

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 convex bases of these dual cones is closed under linear operations. The result offers a new geometric method to analyze quantum states.

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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量