Higher-Rank Numerical Ranges of Unitary and Normal Matrices
Quantum Physics
2008-06-11 v2
Abstract
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary matrix are given by complex polygons determined by the spectral structure of the matrix. We discuss applications of the results to quantum error correction, specifically to the problem of identification and construction of codes for binary unitary noise models.
Keywords
Cite
@article{arxiv.quant-ph/0608244,
title = {Higher-Rank Numerical Ranges of Unitary and Normal Matrices},
author = {Man-Duen Choi and John A. Holbrook and David W. Kribs and Karol Zyczkowski},
journal= {arXiv preprint arXiv:quant-ph/0608244},
year = {2008}
}
Comments
23 pages, 3 figures, preprint version