  The observed IR and the spectator UV particles of a regulated, cutoff quantum
field theory are entangled by their interactions; hence, the IR sector can be
described by the help of the density matrix only. The tree-level renormalized
trajectory is obtained for a self-interacting scalar field theory, containing
the mixed state contributions. One needs a sharp cutoff in the momentum space
as regulator to realize the true loss of information, caused by massive
particles.
