On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases
This paper considers coherent states for the representation of Weyl commutation relations over a field of <i>p</i>-adic numbers. A geometric object, a lattice in vector space over a field of <i>p</i>-adic numbers, corresponds to the family of coherent states. It is proven tha...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/6/902 |
| _version_ | 1797594977403928576 |
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| author | Evgeny Zelenov |
| author_facet | Evgeny Zelenov |
| author_sort | Evgeny Zelenov |
| collection | DOAJ |
| description | This paper considers coherent states for the representation of Weyl commutation relations over a field of <i>p</i>-adic numbers. A geometric object, a lattice in vector space over a field of <i>p</i>-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators. |
| first_indexed | 2024-03-11T02:30:21Z |
| format | Article |
| id | doaj.art-ffafaea1680e44e194b29971f7cca14c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T02:30:21Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ffafaea1680e44e194b29971f7cca14c2023-11-18T10:18:01ZengMDPI AGEntropy1099-43002023-06-0125690210.3390/e25060902On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased BasesEvgeny Zelenov0Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, RussiaThis paper considers coherent states for the representation of Weyl commutation relations over a field of <i>p</i>-adic numbers. A geometric object, a lattice in vector space over a field of <i>p</i>-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators.https://www.mdpi.com/1099-4300/25/6/902<i>p</i>-adic quantum theorymutually unbiased basesHadamard matrix |
| spellingShingle | Evgeny Zelenov On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases Entropy <i>p</i>-adic quantum theory mutually unbiased bases Hadamard matrix |
| title | On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases |
| title_full | On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases |
| title_fullStr | On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases |
| title_full_unstemmed | On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases |
| title_short | On Geometry of <i>p</i>-Adic Coherent States and Mutually Unbiased Bases |
| title_sort | on geometry of i p i adic coherent states and mutually unbiased bases |
| topic | <i>p</i>-adic quantum theory mutually unbiased bases Hadamard matrix |
| url | https://www.mdpi.com/1099-4300/25/6/902 |
| work_keys_str_mv | AT evgenyzelenov ongeometryofipiadiccoherentstatesandmutuallyunbiasedbases |