  We study the Wigner function for the inflationary tensor perturbation defined
in the real phase space. We compute explicitly the Wigner function including
the contributions from the cubic self-interaction Hamiltonian of tensor
perturbations. Then we argue that it is no longer an appropriate description
for the probability distribution in the sense that quantum nature allows
negativity around vanishing phase variables. This comes from the non-Gaussian
wavefunction in the mixed state as a result of the non-linear interaction
between super- and sub-horizon modes. We also show that this is related to the
explicit infrared divergence in the Wigner function, in contrast to the trace
of the density matrix.
