Almost all multipartite qubit quantum states have trivial stabilizer

Understand

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.