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

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Range criterion and classification of true entanglement in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mi>M</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math>system

Range criterion and classification of true entanglement in a2×M×Nsystem