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arXiv · 1905.10873

On the role of Hermite-like polynomials in the Fock representations of Gaussian states

Gianfranco Cariolaro·Giuseppe Dattoli·Gianfranco Pierobon
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Abstract

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.

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Gianfranco Cariolaro, Giuseppe Dattoli, Gianfranco Pierobon. 2019-05-26. On the role of Hermite-like polynomials in the Fock representations of Gaussian states. https://doi.org/10.1063/1.5127516

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