Matrix systems, algebras, and open maps

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2025年6月1日

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Stephan Weis

摘要

Every state on the algebra $\textrm{M}_n$ $M_{n}$ of complex $n\times n$ $n \times n$ matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that the restriction to every *-subalgebra of $\textrm{M}_n$ $M_{n}$ is open. This simplifies topology problems in matrix theory and quantum information theory.