dorsal/arxiv
View SchemaHigher-Rank Numerical Ranges of Unitary and Normal Matrices
| Authors | Man-Duen Choi, John A. Holbrook, David W. Kribs, Karol Zyczkowski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608244 |
| URL | https://arxiv.org/abs/quant-ph/0608244 |
| Journal | Operators and Matrices 1, 409-426 (2007) |
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.
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"abstract": "We verify a conjecture on the structure of higher-rank numerical ranges for a\nwide class of unitary and normal matrices. Using analytic and geometric\ntechniques, we show precisely how the higher-rank numerical ranges for a\ngeneric unitary matrix are given by complex polygons determined by the spectral\nstructure of the matrix. We discuss applications of the results to quantum\nerror correction, specifically to the problem of identification and\nconstruction of codes for binary unitary noise models.",
"arxiv_id": "quant-ph/0608244",
"authors": [
"Man-Duen Choi",
"John A. Holbrook",
"David W. Kribs",
"Karol Zyczkowski"
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"quant-ph"
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"journal_ref": "Operators and Matrices 1, 409-426 (2007)",
"title": "Higher-Rank Numerical Ranges of Unitary and Normal Matrices",
"url": "https://arxiv.org/abs/quant-ph/0608244"
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