On local invariants of pure three-qubit states

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension six. We show that there is no set of six algebraically independent polynomial invariants of degree ⩽ 6, and find such a set with maximum degree eight. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.