H. F. Chau
Published 2010-06-18, updated 2011-07-06Version 2
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.
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
Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time
Quantum propagator and characteristic equation in the presence of a chain of $δ$-potentials
The Dirac-Moshinsky Oscillator: Theory and Applications
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