2010•arXiv (Cornell University)Open access

Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices

H. F. Chau

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.

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Key concepts: Unitary state, Commutative property, Unitary transformation, Degree (music), Unitary matrix, Mathematics, Pure mathematics, Limit (mathematics)