Multilinear singular value decomposition for two qubits

Schmidt decomposition has been used in the local unitary (lu) classification of bipartite quantum states for some time. in order to generalize the lu classification of bipartite quantum states into multipartite quantum states,higher order singular value decomposition (hosvd) is introduced but specific examples have not been explicitly worked out. in this pedagogical paper,we would like to work out such details in two qubits since the lu classification of two qubits is well known. we first demonstrate the method of hosvd in two-qubit systems and discuss its properties. in terms of the lu classification of two-qubit states,some subtle differences in the stabilizer groups of entanglement classes are noticed when schmidt decomposition is substituted by hosvd. to reconcile the differences between the two,further studies are needed.