Elementary proofs of two theorems involving arguments of eigenvalues of a product of two unitary matrices
<p>Abstract</p> <p>We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices--one by Childs et al. [J. Mod. Phys. <b>47</b>, 155 (2000)] and the other one by Chau [Quant. Inf. Comp. <b&...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2011/1/18 |
| Summary: | <p>Abstract</p> <p>We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices--one by Childs et al. [J. Mod. Phys. <b>47</b>, 155 (2000)] and the other one by Chau [Quant. Inf. Comp. <b>11</b>, 721 (2011)]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.</p> |
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| ISSN: | 1025-5834 1029-242X |