  The stabilizer group of an n-qubit state \psi is the set of all matrices of
the form g=g_1\otimes\cdots\otimes g_n, with g_1,...,g_n being any 2x2
invertible complex matrices, that satisfy g\psi=\psi. We show that for 5 or
more qubits, except for a set of states of zero measure, the stabilizer group
of multipartite entangled states is trivial; that is, containing only the
identity element. We use this result to show that for 5 or more qubits, the
action of deterministic local operations and classical communication (LOCC) can
almost always be simulated simply by local unitary (LU) operations. This proves
that almost all n-qubit states with n>4 are isolated, that is they can neither
be reached nor converted into any other (n-partite entangled), LU-inequivalent
state via deterministic LOCC. We also find a simple and elegant expression for
the maximal probability to convert one multi-qubit entangled state to another
for this generic set of states.
