Kippenhahn's Theorem for joint numerical ranges and quantum states. (arXiv:1907.04768v1 [math.AG])

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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