Mutually orthogonal unitary and orthogonal matrices
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| Titel: | Mutually orthogonal unitary and orthogonal matrices |
|---|---|
| Autoren: | Zhiwei Song, Lin Chen, Saiqi Liu |
| Quelle: | Linear Algebra and its Applications. 725:1-17 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Elsevier BV, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | Quantum Physics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Mathematical Physics |
| Beschreibung: | We introduce the concept of n-OU and n-OO matrix sets, a collection of n mutually-orthogonal unitary and real orthogonal matrices under Hilbert-Schmidt inner product. We give a detailed characterization of order-three n-OO matrix sets under orthogonal equivalence. As an application in quantum information theory, we show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively. Further, we propose a new matrix decomposition approach, defining an n-OU (resp. n-OO) decomposition for a matrix as a linear combination of n matrices from an n-OU (resp. n-OO) matrix set. We show that any order-d matrix has a d-OU decomposition. As a contrast, we provide criteria for an order-three real matrix to possess an n-OO decomposition. 16 pages, no figure |
| Publikationsart: | Article |
| Sprache: | English |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2025.06.025 |
| DOI: | 10.48550/arxiv.2309.11128 |
| Zugangs-URL: | http://arxiv.org/abs/2309.11128 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Dokumentencode: | edsair.doi.dedup.....3ff74d3d02adb51f11eb41b8f559948d |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | We introduce the concept of n-OU and n-OO matrix sets, a collection of n mutually-orthogonal unitary and real orthogonal matrices under Hilbert-Schmidt inner product. We give a detailed characterization of order-three n-OO matrix sets under orthogonal equivalence. As an application in quantum information theory, we show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively. Further, we propose a new matrix decomposition approach, defining an n-OU (resp. n-OO) decomposition for a matrix as a linear combination of n matrices from an n-OU (resp. n-OO) matrix set. We show that any order-d matrix has a d-OU decomposition. As a contrast, we provide criteria for an order-three real matrix to possess an n-OO decomposition.<br />16 pages, no figure |
|---|---|
| ISSN: | 00243795 |
| DOI: | 10.1016/j.laa.2025.06.025 |