  We explore the connection between quantum brachistochrone (time-optimal)
evolution of a three-qubit system and its residual entanglement called
three-tangle. The result shows that the entanglement between two qubits is not
required for some brachistochrone evolutions of a three-qubit system. However,
the evolution between two distinct states cannot be implemented without its
three-tangle, except for the trivial cases in which less than three qubits
attend evolution. Although both the probability density function of the
time-averaged three-tangle and that of the time-averaged squared concurrence
between two subsystems become more and more uniform with the decrease in angles
of separation between an initial state and a final state, the features of their
most probable values exhibit a different trend.
