  By introducing the thermo entangled state representation, we convert the
calculation of Wigner function (WF) of density operator to an overlap between
"two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a
new WF evolution formula of any initial state in self-Kerr Medium with photon
loss and find that the photon number distribution for any initial state is
independent of the coupling factor with Kerr Medium, where the number state is
not affected by the Kerr nonlinearity and evolves into a density operator of
binomial distribution.
