  Completely positive quantum operations are frequently discussed in the
contexts of statistical mechanics and quantum information. They are customarily
given by maps forming positive operator-values measures. To intuitively
understand physical meanings of such abstract operations, the method of
phase-space representations is examined. This method enables one to grasp the
operations in terms of the classical statistical notions. As an example of
physical importance, here, the phase-space representation of the completely
positive quantum operation arising from the single-mode subdynamics of the
two-mode squeezed vacuum state, which maps from the vacuum state at vanishing
temperature to mixed states with perfect decoherence including the thermal
state, is studied. It is found in the $P$ representation that remarkably this
operation is invertible, implying that coherence lost by the quantum operation
can be recovered.
