Mutually unbiased unitary bases
We consider the notion of unitary transformations forming bases for subspaces of M(d,C) such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimens...
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| Format: | Article |
| Language: | English English |
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American Physical Society
2016
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| Online Access: | http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/1/PhysRevA.94.052328.pdf http://irep.iium.edu.my/53093/7/53093_Mutually%20unbiased_scopus.pdf |
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| author | Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano |
| author_facet | Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano |
| author_sort | Shamsul Shaari, Jesni |
| building | IIUM Repository |
| collection | Online Access |
| description | We consider the notion of unitary transformations forming bases for subspaces of M(d,C) such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimensional subspaces while proving the nonexistence of such a construction for the three-dimensional case. Extending this to higher dimensions, we commit to such a construct for the case of qutrits and provide evidence for the existence of such unitaries for prime dimensional quantum systems. Focusing on the qubit case, we show that the average fidelity for estimating any such transformation is equal to the case for estimating a completely unknown unitary from SU(2). This is then followed by a quick application for such unitaries in a quantum cryptographic setup. |
| first_indexed | 2025-11-14T16:33:05Z |
| format | Article |
| id | iium-53093 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:33:05Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-530932017-10-21T07:02:36Z http://irep.iium.edu.my/53093/ Mutually unbiased unitary bases Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano QC Physics We consider the notion of unitary transformations forming bases for subspaces of M(d,C) such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimensional subspaces while proving the nonexistence of such a construction for the three-dimensional case. Extending this to higher dimensions, we commit to such a construct for the case of qutrits and provide evidence for the existence of such unitaries for prime dimensional quantum systems. Focusing on the qubit case, we show that the average fidelity for estimating any such transformation is equal to the case for estimating a completely unknown unitary from SU(2). This is then followed by a quick application for such unitaries in a quantum cryptographic setup. American Physical Society 2016-11-21 Article PeerReviewed application/pdf en http://irep.iium.edu.my/53093/1/PhysRevA.94.052328.pdf application/pdf en http://irep.iium.edu.my/53093/7/53093_Mutually%20unbiased_scopus.pdf Shamsul Shaari, Jesni and N. M. Nasir, Rinie and Mancini, Stefano (2016) Mutually unbiased unitary bases. Physical Review A, 94 (5). 052328-1. ISSN 2469-9926 E-ISSN 2469-9934 http://journals.aps.org/pra/ 10.1103/PhysRevA.94.052328 |
| spellingShingle | QC Physics Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano Mutually unbiased unitary bases |
| title | Mutually unbiased unitary bases |
| title_full | Mutually unbiased unitary bases |
| title_fullStr | Mutually unbiased unitary bases |
| title_full_unstemmed | Mutually unbiased unitary bases |
| title_short | Mutually unbiased unitary bases |
| title_sort | mutually unbiased unitary bases |
| topic | QC Physics |
| url | http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/1/PhysRevA.94.052328.pdf http://irep.iium.edu.my/53093/7/53093_Mutually%20unbiased_scopus.pdf |