Classification of multipartite entanglement containing infinitely many kinds of states
Lin Chen, Yixin Chen, Yu-Xue Mei · Physical Review A · 2006
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 $2\ifmmode\times\else\texttimes\fi{}M\ifmmode\times\else\texttimes\fi{}N$ states under reversible local filtering operations. By using these techniques, we entirely classify the family of $2\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4$ states, which actually contains infinitely many kinds of states. The classifications of true entanglement of $2\ifmmode\times\else\texttimes\fi{}(M+3)\ifmmode\times\else\texttimes\fi{}(2M+3)$ and $2\ifmmode\times\else\texttimes\fi{}(M+4)\ifmmode\times\else\texttimes\fi{}(2M+4)$ systems are briefly listed, respectively.