Kippenhahn's Theorem for joint numerical ranges and quantum states

Autor:	Plaumann, Daniel, Sinn, Rainer, Weis, Stephan
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Geometry Mathematics - Operator Algebras Quantum Physics 47A12 14P10 52A20 81P99
Zdroj:	SIAM Journal on Applied Algebra and Geometry 5:1 (2021), 86-113
Druh dokumentu:	Working Paper
DOI:	10.1137/19M1286578
Popis:	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. Comment: 28 pages, 5 figures; version v2 extends version v1 in applications and examples and has more detailed proofs. Any comments are welcomed
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.04768 Zobrazit plný text záznamu View this record from Arxiv