  Exploring an analytical expression for the convex roof of the pure state
squared concurrence for rank 2 mixed states the entanglement of a system of
three particles under decoherence is studied, using the monogamy inequality for
mixed states and the residual entanglement obtained from it. The monogamy
inequality is investigated both for the concurrence and the negativity in the
case of local independent phase damping channel acting on generalized GHZ
states of three particles and the local independent amplitude damping channel
acting on generalized W state of three particles. It is shown that the
bipartite entanglement between one qubit and the rest has a qualitative similar
behavior to the entanglement between individual qubits, and that the residual
entanglement in terms of the negativity cannot be a good entanglement measure
for mixed states, since it can increase under local decoherence.
