On mutually unbiased unitary bases in prime-dimensional Hilbert spaces
Akin to the idea of complete sets of mutually unbiased bases for prime-dimensional Hilbert spaces, Hd, we study its analogue for a d-dimensional subspace of M(d,C), i.e. mutually unbiased unitary bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces...
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Springer US
2019
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| Online Access: | http://irep.iium.edu.my/71981/ http://irep.iium.edu.my/71981/1/71981_On%20mutually%20unbiased%20unitary.pdf http://irep.iium.edu.my/71981/7/71981%20On%20mutually%20unbiased%20unitary%20bases%20%20SCOPUS.pdf http://irep.iium.edu.my/71981/13/71981_On%20mutually%20unbiased%20unitary%20bases%20in%20prime-dimensional%20Hilbert%20spaces_wos.pdf |
| _version_ | 1848787543632379904 |
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| author | Nasir, Rinie N. M. Shamsul Shaari, Jesni Mancini, Stefano |
| author_facet | Nasir, Rinie N. M. Shamsul Shaari, Jesni Mancini, Stefano |
| author_sort | Nasir, Rinie N. M. |
| building | IIUM Repository |
| collection | Online Access |
| description | Akin to the idea of complete sets of mutually unbiased bases for prime-dimensional Hilbert spaces, Hd, we study its analogue for a d-dimensional subspace of M(d,C), i.e. mutually unbiased unitary bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces and beyond that, we define a relevant monoid structure for Hd isomorphic to one for the subspace of M(d,C). This provides us not only with the maximal number of such MUUBs, but also a recipe for its construction. |
| first_indexed | 2025-11-14T17:26:36Z |
| format | Article |
| id | iium-71981 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:26:36Z |
| publishDate | 2019 |
| publisher | Springer US |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-719812019-08-01T04:13:06Z http://irep.iium.edu.my/71981/ On mutually unbiased unitary bases in prime-dimensional Hilbert spaces Nasir, Rinie N. M. Shamsul Shaari, Jesni Mancini, Stefano QA155 Algebra QC Physics Akin to the idea of complete sets of mutually unbiased bases for prime-dimensional Hilbert spaces, Hd, we study its analogue for a d-dimensional subspace of M(d,C), i.e. mutually unbiased unitary bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces and beyond that, we define a relevant monoid structure for Hd isomorphic to one for the subspace of M(d,C). This provides us not only with the maximal number of such MUUBs, but also a recipe for its construction. Springer US 2019-04-29 Article PeerReviewed application/pdf en http://irep.iium.edu.my/71981/1/71981_On%20mutually%20unbiased%20unitary.pdf application/pdf en http://irep.iium.edu.my/71981/7/71981%20On%20mutually%20unbiased%20unitary%20bases%20%20SCOPUS.pdf application/pdf en http://irep.iium.edu.my/71981/13/71981_On%20mutually%20unbiased%20unitary%20bases%20in%20prime-dimensional%20Hilbert%20spaces_wos.pdf Nasir, Rinie N. M. and Shamsul Shaari, Jesni and Mancini, Stefano (2019) On mutually unbiased unitary bases in prime-dimensional Hilbert spaces. Quantum Information Processing, 18. pp. 1-16. ISSN 1570-0755 E-ISSN 1573-1332 https://link.springer.com/article/10.1007/s11128-019-2298-2 10.1007/s11128-019-2298-2 |
| spellingShingle | QA155 Algebra QC Physics Nasir, Rinie N. M. Shamsul Shaari, Jesni Mancini, Stefano On mutually unbiased unitary bases in prime-dimensional Hilbert spaces |
| title | On mutually unbiased unitary bases in prime-dimensional Hilbert spaces |
| title_full | On mutually unbiased unitary bases in prime-dimensional Hilbert spaces |
| title_fullStr | On mutually unbiased unitary bases in prime-dimensional Hilbert spaces |
| title_full_unstemmed | On mutually unbiased unitary bases in prime-dimensional Hilbert spaces |
| title_short | On mutually unbiased unitary bases in prime-dimensional Hilbert spaces |
| title_sort | on mutually unbiased unitary bases in prime-dimensional hilbert spaces |
| topic | QA155 Algebra QC Physics |
| url | http://irep.iium.edu.my/71981/ http://irep.iium.edu.my/71981/ http://irep.iium.edu.my/71981/ http://irep.iium.edu.my/71981/1/71981_On%20mutually%20unbiased%20unitary.pdf http://irep.iium.edu.my/71981/7/71981%20On%20mutually%20unbiased%20unitary%20bases%20%20SCOPUS.pdf http://irep.iium.edu.my/71981/13/71981_On%20mutually%20unbiased%20unitary%20bases%20in%20prime-dimensional%20Hilbert%20spaces_wos.pdf |