Hermite Polynomial Representation of the Spin States

TL;DR

This paper introduces a Hermite polynomial-based quasiprobability distribution for spin states, establishing connections with electromagnetic field oscillators and spin tomography, and addressing magnetic moment rotation.

Contribution

It presents a novel invertible mapping of spin states onto quasiprobability distributions using Hermite polynomials, linking spin and optical systems.

Findings

Constructed an invertible map of spin states onto quasiprobability distributions.

Derived an inversion formula for the spin-density matrix using Hermite polynomials.

Explored the relation between spin tomography and the proposed representation.

Abstract

The invertable map of spin state density operator onto quasiprobability distribution of three continuous variables is constructed. The connection with two-mode electromagnetic field oscillators is discussed. The inversion formula for spin-density matrix is given in terms of Hermite polynomials. The connection with the spin-tomographic representation is examined. The problem of the magnetic moment rotation in the magnetic field is considered in the suggested representation of spin states.