A 2-categorical approach to composing quantum structures
We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categori...
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| Format: | Conference item |
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Schloss Dagstuhl
2017
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| _version_ | 1797064756442431488 |
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| author | Reutter, D Vicary, J |
| author_facet | Reutter, D Vicary, J |
| author_sort | Reutter, D |
| collection | OXFORD |
| description | We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method. |
| first_indexed | 2024-03-06T21:18:54Z |
| format | Conference item |
| id | oxford-uuid:40c2e236-4573-4916-97ca-97c17f4f79ae |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:18:54Z |
| publishDate | 2017 |
| publisher | Schloss Dagstuhl |
| record_format | dspace |
| spelling | oxford-uuid:40c2e236-4573-4916-97ca-97c17f4f79ae2022-03-26T14:39:44ZA 2-categorical approach to composing quantum structuresConference itemhttp://purl.org/coar/resource_type/c_5794uuid:40c2e236-4573-4916-97ca-97c17f4f79aeSymplectic Elements at OxfordSchloss Dagstuhl2017Reutter, DVicary, JWe present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method. |
| spellingShingle | Reutter, D Vicary, J A 2-categorical approach to composing quantum structures |
| title | A 2-categorical approach to composing quantum structures |
| title_full | A 2-categorical approach to composing quantum structures |
| title_fullStr | A 2-categorical approach to composing quantum structures |
| title_full_unstemmed | A 2-categorical approach to composing quantum structures |
| title_short | A 2-categorical approach to composing quantum structures |
| title_sort | 2 categorical approach to composing quantum structures |
| work_keys_str_mv | AT reutterd a2categoricalapproachtocomposingquantumstructures AT vicaryj a2categoricalapproachtocomposingquantumstructures AT reutterd 2categoricalapproachtocomposingquantumstructures AT vicaryj 2categoricalapproachtocomposingquantumstructures |