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Multi-Dimensional Hermite Polynomials in Quantum Optics

Pieter Kok·Samuel L Braunstein
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Abstract

We study a class of optical circuits with vacuum input states consisting of Gaussian sources without coherent displacements such as down-converters and squeezers, together with detectors and passive interferometry (beam-splitters, polarisation rotations, phase-shifters etc.). We show that the outgoing state leaving the optical circuit can be expressed in terms of so-called multi-dimensional Hermite polynomials and give their recursion and orthogonality relations. We show how quantum teleportation of photon polarisation can be modelled using this description.

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Pieter Kok, Samuel L Braunstein. 2000-11-30. Multi-Dimensional Hermite Polynomials in Quantum Optics. https://doi.org/10.1088/0305-4470%2F34%2F31%2F312

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