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Acta Sinica Quantum Optica

A New Approach for Deriving the Bipartite Entangled State Representation

YU Zhi-song

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

For the bipartite entangled state representation in quantum optics,the author present a new approach to analyze its expression in Fock space.The analysis naturally leads to the introduction of two-variable Hermite polynomials,which is sharply different with the usual single-variable Hermite polynomials.

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By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
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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.