On the role of Hermite-like polynomials in the Fock representations of Gaussian states
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866914814340628480 |
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| author | Cariolaro, Gianfranco Dattoli, Giuseppe Pierobon, Gianfranco |
| author_facet | Cariolaro, Gianfranco Dattoli, Giuseppe Pierobon, Gianfranco |
| contents | The expansion of quantum states and operators in terms of Fock states plays a fundamental role in the field of continuous-variable quantum mechanics. In particular, for general single-mode Gaussian operators and Gaussian noisy states, many different approaches have been used in the evaluation of their Fock representation. In this paper a natural approach has been applied using exclusively the operational properties of the Hermite and Hermite-like polynomials and showing their fundamental role in this field. Closed-form results in terms of polynomials, exponentials, and simple algebraic functions are the major contribution of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_10873 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the role of Hermite-like polynomials in the Fock representations of Gaussian states Cariolaro, Gianfranco Dattoli, Giuseppe Pierobon, Gianfranco Quantum Physics The expansion of quantum states and operators in terms of Fock states plays a fundamental role in the field of continuous-variable quantum mechanics. In particular, for general single-mode Gaussian operators and Gaussian noisy states, many different approaches have been used in the evaluation of their Fock representation. In this paper a natural approach has been applied using exclusively the operational properties of the Hermite and Hermite-like polynomials and showing their fundamental role in this field. Closed-form results in terms of polynomials, exponentials, and simple algebraic functions are the major contribution of the paper. |
| title | On the role of Hermite-like polynomials in the Fock representations of Gaussian states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/1905.10873 |