Two-variable Hermite Polynomial State and Its Wigner Function

摘要

In this paper we obtain the Wigner functions of two-variable Hermite polynomial states (THPS) and their marginal distribution using the entangled state |ξ〉 representation. Also we obtain tomogram of THPS by virtue of the Radon transformation between the Wigner operator and the projection operator of another entangled state |η,τ ₁,τ ₂〉. Keywords Two-variable Hermite polynomial state - Entangled state representation - Wigner function - Tomogram function Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation of Shandong Province of China under Grant Y2008A23.