  Non-positive, Markovian semigroups are sometimes used to describe the time
evolution of subsystems immersed in an external environment. A widely adopted
prescription to avoid the appearance of negative probabilities is to eliminate
from the admissible initial conditions those density matrices that would not
remain positive by the action of the semigroup dynamics. Using a continuous
variable model, we show that this procedure leads to physical inconsistencies
when two subsystems are considered and their initial state is entangled.
