Multi-Dimensional Hermite Polynomials in Quantum Optics

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.

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

References in corpus (1)

• Experimental quantum teleportation

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