For mixed quantum states, entanglement can be characterized by a quotient group of local unitary stabilizers of the density matrix, and any nontriviality for separable states must come from multipartite entanglement with the purifying system.
Local symmetry properties of pure 3-qubit states
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Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.
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Entanglement groups for mixed states
For mixed quantum states, entanglement can be characterized by a quotient group of local unitary stabilizers of the density matrix, and any nontriviality for separable states must come from multipartite entanglement with the purifying system.