  We investigate the speed of disentanglement in the multiqubit systems under
the local depolarizing channel, in which each qubit is independently coupled to
the environment. We focus on the bipartition entanglement between one qubit and
the remaining qubits constituting the system, which is measured by the
negativity. For the two-qubit system, the speed for the pure state completely
depends on its entanglement. The upper and lower bounds of the speed for
arbitrary two-qubit states, and the necessary conditions for a state achieving
them, are obtained. For the three-qubit system, we study the speed for pure
states, whose entanglement properties can be completely described by five
local-unitary-transformation invariants. An analytical expression of the
relation between the speed and the invariants is derived. The speed is enhanced
by the the three-tangle which is the entanglement among the three qubits, but
reduced by the the two-qubit correlations outside of the concurrence. The decay
of the negativity can be restrained by the other two negativity with the
coequal sense. The unbalance between two qubits can reduce speed of
disentanglement of the remaining qubit in the system, even can retrieve the
entanglement partially. For the k-qubit systems in an arbitrary superposition
of GHZ state and W state, the speed depends almost entirely on the amount of
the negativity when k increases to five or six. An alternative quantitative
definition for the robustness of entanglement is presented based on the speed
of disentanglement, with comparison to the widely studied robustness measured
by the critical amount of noise parameter where the entanglement vanishes. In
the limit of large number of particles, the alternative robustness of the
GHZ-type states is inversely proportional to k, and the one of the W states
approaches 1/\sqrt{k}.
