Classification of multipartite entanglement containing infinitely many kinds of states

We give a further investigation of the range criterion and low-to-high rank generating mode introduced in Chen and Chen [Phys. Rev. A 73, 052310 (2006)], which can be used for the classification of 2×M×N states under reversible local filtering operations. By using these techniques, we entirely classify the family of 2×4×4 states, which actually contains infinitely many kinds of states. The classifications of true entanglement of 2×(M+3)×(2M+3) and 2×(M+4)×(2M+4) systems are briefly listed, respectively.