  We study the behaviour of Husimi, Wigner and T{\"o}plitz symbols of quantum
density matrices when quantum statistics are tested on them, that is when on
exchange two coordinates in one of the two variables of their integral kernel.
We show that to each of these actions is associated a canonical transform on
the cotangent bundle of the underlying classical phase space. Equivalently can
one associate a complex canonical transform on the complexification of the
phase-space. In the off-diagonal T{\"o}plitz representation introduced in [P],
the action considered is associated to a complex aanticanonical relation.
