Multi-Dimensional Hermite Polynomials in Quantum Optics

Details Multi-Dimensional Hermite Polynomials in Quantum Optics Multi-Dimensional Hermite Polynomials in Quantum Optics

2000-11-29

arxiv.org/abs/quant-ph/0011114v2

J. Phys. A 34, 6185 (2001)

Physics

Quantum Physics

10 pages, submitted to J. Phys. A, removed spurious file

Scientific paper

10.1088/0305-4470/34/31/312

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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