  We construct a distinct class of nonlinear displaced Kerr state by
application of the displacement operator upon a state which is prepared by
sending the well-known photon-added coherent state through a normal Kerr
medium. A sketch for the experimental set-up for preparing the state is
suggested. We evaluate some statistical properties such as the photon number
distribution, Mandel's $Q$ parameter, Husimi-$Q$ and Wigner functions, and
quadrature squeezing, for the nonlinear displaced Kerr state, and then analyze
the nonclassicality in terms of these standard parameters. We reduce the
infinite-level problem to a truncated discrete two-level system by using low
Kerr parameter approximation and then convert the generated nonclassicality
into bipartite entanglement between the two modes of an output state of a
linear optical device.
