Range criterion and classification of true entanglement in $2\times{M}\times{N}$ system

Abstract

We propose a range criterion which is a sufficient and necessary condition satisfied by two pure states transformable with each other under reversible stochastic local operations assisted with classical communication. We also provide a systematic method for seeking all kinds of true entangled states in the $2\times{M}\times{N}$ system, and can effectively distinguish them by means of the range criterion. The efficiency of the criterion and the method is exhibited by the classification of true entanglement in some types of the tripartite systems.Comment: 7 papes, no figure, Revtex. This is the published versio