Quantum Latin squares and unitary error bases
In this paper we introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares, and investigate their applications in quantum computer science. Our main results are on applications to unitary error bases (UEBs), basic structures in quantum information which...
| Váldodahkkit: | , |
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| Materiálatiipa: | Journal article |
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Rinton Press
2016
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| _version_ | 1826299099698167808 |
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| author | Musto, B Vicary, J |
| author_facet | Musto, B Vicary, J |
| author_sort | Musto, B |
| collection | OXFORD |
| description | In this paper we introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares, and investigate their applications in quantum computer science. Our main results are on applications to unitary error bases (UEBs), basic structures in quantum information which lie at the heart of procedures such as teleportation, dense coding and error correction. We present a new method for constructing a UEB from a quantum Latin square equipped with extra data. Developing construction techniques for UEBs has been a major activity in quantum computation, with three primary methods proposed: shift-andmultiply, Hadamard, and algebraic. We show that our new approach simultaneously generalizes the shift-and-multiply and Hadamard methods. Furthermore, we explicitly construct a UEB using our technique which we prove cannot be obtained from any of these existing methods. |
| first_indexed | 2024-03-07T04:56:46Z |
| format | Journal article |
| id | oxford-uuid:d6de046d-30f1-4a6f-a857-173989a4e9a2 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:56:46Z |
| publishDate | 2016 |
| publisher | Rinton Press |
| record_format | dspace |
| spelling | oxford-uuid:d6de046d-30f1-4a6f-a857-173989a4e9a22022-03-27T08:36:52ZQuantum Latin squares and unitary error basesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d6de046d-30f1-4a6f-a857-173989a4e9a2Symplectic Elements at OxfordRinton Press2016Musto, BVicary, JIn this paper we introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares, and investigate their applications in quantum computer science. Our main results are on applications to unitary error bases (UEBs), basic structures in quantum information which lie at the heart of procedures such as teleportation, dense coding and error correction. We present a new method for constructing a UEB from a quantum Latin square equipped with extra data. Developing construction techniques for UEBs has been a major activity in quantum computation, with three primary methods proposed: shift-andmultiply, Hadamard, and algebraic. We show that our new approach simultaneously generalizes the shift-and-multiply and Hadamard methods. Furthermore, we explicitly construct a UEB using our technique which we prove cannot be obtained from any of these existing methods. |
| spellingShingle | Musto, B Vicary, J Quantum Latin squares and unitary error bases |
| title | Quantum Latin squares and unitary error bases |
| title_full | Quantum Latin squares and unitary error bases |
| title_fullStr | Quantum Latin squares and unitary error bases |
| title_full_unstemmed | Quantum Latin squares and unitary error bases |
| title_short | Quantum Latin squares and unitary error bases |
| title_sort | quantum latin squares and unitary error bases |
| work_keys_str_mv | AT mustob quantumlatinsquaresandunitaryerrorbases AT vicaryj quantumlatinsquaresandunitaryerrorbases |