  Non-positive Markov approximations are sometimes used to describe the
dynamics of qubits in weak interaction with suitable environments; the
appearance of negative probabilities is avoided by assuming that the transient
regime eliminates from the possible initial conditions those qubit states which
would otherwise be mapped out of the Bloch sphere by the subsequent Markovian
time-evolution. By means of a simple model, we discuss some physical
inconsistencies of this approach in relation to entanglement; in particular, we
show that slipped non-positive reduced dynamics might create entanglement
through a purely local action.
