Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices
Abstract
By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found. Interestingly, this family of metrics can be naturally converted into useful indicators of the degree of non-commutativity between two unitary matrices.
Cite
@article{arxiv.1006.3614,
title = {Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices},
author = {H. F. Chau},
journal= {arXiv preprint arXiv:1006.3614},
year = {2011}
}
Comments
13 pages in RevTex 4.1, 2 figures, to appear in QIC. This replacement concentrates only on the more physics and quantum information aspects of the results reported in the original manuscript with a more detailed proof. The mathematical results involving the discovery of several matrix inequalities reported in the original version will be strengthened and rewritten in a separate posting