Mutually-orthogonal unitary and orthogonal matrices
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912671150899200 |
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| author | Song, Zhiwei Chen, Lin Liu, Saiqi |
| author_facet | Song, Zhiwei Chen, Lin Liu, Saiqi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11128 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mutually-orthogonal unitary and orthogonal matrices Song, Zhiwei Chen, Lin Liu, Saiqi Quantum Physics Mathematical Physics 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. |
| title | Mutually-orthogonal unitary and orthogonal matrices |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2309.11128 |