Almost all multipartite qubit quantum states have trivial stabilizer

The stabilizer group of an n-qubit state vertical bar psi > is the set of all matrices of the form g = g(1) circle times ... circle times g(n), with g(1), ... , g(n) being any 2 x 2 invertible complex matrices that satisfy g vertical bar psi > = vertical bar 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 >= 5 can neither be reached nor be 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. Published by AIP Publishing.