  We propose two experimental schemes that can produce an arbitrary
photon-number entangled state (PNES) in a finite dimension. This class of
entangled states naturally includes non-Gaussian continuous-variable (CV)
states that may provide some practical advantages over the Gaussian
counterparts (two-mode squeezed states). We particularly compare the
entanglement characteristics of the Gaussian and the non-Gaussian states in
view of the degree of entanglement and the Einstein-Podolsky-Rosen correlation,
and further discuss their applications to the CV teleportation and the
nonlocality test. The experimental imperfection due to the on-off
photodetectors with nonideal efficiency is also considered in our analysis to
show the feasibility of our schemes within existing technologies.
