On local invariants of pure three-qubit states

Abstract

Being a study of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. It is shown that there is no set of six independent polynomial invariants of degree less than or equal to 6, and such a set with maximum degree 8 is exhibited. An intrinsic definition of a canonical state on each orbit is described, and the (non-polynomial) invariants associated with it are discussed.