Quantum computing, higher rank numerical ranges, totally isotropic subspaces, and matrix equations
Professor Chi Kwong Li 李志光 教授Department of Mathematics, College of William and Mary, USA 下午 3:00–4:00 鴻經館 107 室 Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of closed half planes (of complex numbers). As a result, it is always a convex set in C. Moreover, the higher rank numerical range of a normal matrix is a convex polygon determined by the eigenvalues. These two consequences confirm the conjectures of Choi et al on the subject. In addition, the results are used to derive a formula for the maximum dimension of a totally isotropic subspace of a square matrix, and verify the solvability of certain matrix equations.
This is joint work with Nung-Sing Sze, University of Connecticut.