  The separability of bipartite non-Gaussian states is studied by applying the
realignment criterion with the technique of functional analysis. The
realignment criterion is given as one inequality in contrast to the infinitive
number of inequalities based on the moments. We give the necessary and
sufficient condition of inseparability for non-Gaussian states prepared by
photon subtraction or addition from symmetric Gaussian states. The entanglement
criterion of non-Gaussian states evolved in thermal noise and amplitude damping
environment is also obtained.
