  A scheme for conditional generating a Hermite polynomial excited squeezed
vacuum states (HESVS) is proposed. Injecting a two-mode squeezed vacuum state
(TMSVS) into a beam splitter (BS) and counting the photons in one of the output
channels, the conditional state in the other output channel is just a HESVS. To
exhibit a number of nonclassical effects and non-Guassianity, we mainly
investigate the photon number distribution, sub-Poissonian distribution,
quadrature component distribution, and quasi-probability distribution of the
HPESVS. We find that its nonclassicality closely relates to the control
parameter of the BS, the squeezed parameter of the TMSVS, and the photon number
of conditional measurement. These further demonstrate that performing the
conditional measurement on a BS is an effective approach to generate
non-Guassian state.
