Quantum Erasure of Decoherence
Open Systems & Information Dynamics
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An $n\times n$ complex Hermitian or real symmetric matrix is a correlation matrix if it is positive semidefinite and all its diagonal entries equal one. The collection of all $n\times n$ correlation matrices forms a compact convex set. The extreme points of this convex set are called extreme correlation matrices. In this note, elementary techniques are used to obtain a characterization of extreme correlation matrices and a canonical form for correlation matrices. Using these results, the authors deduce most of the existing results on this topic, simplify a construction of extreme correlation matrices proposed by Grone, Pierce, and Watkins, and derive an efficient algorithm for checking extreme correlation matrices.