Classification of the entangled states of $$2 \times L \times M \times N$$ 2 × L × M × N

We present a practical entanglement classification scheme for pure state in form of $$2\times L\times M\times N$$2×L×M×N under the stochastic local operation and classical communication (SLOCC), where every inequivalent class of the entangled quantum states may be sorted out according to its standard form and the corresponding transformation matrix. This provides a practical method for determining the interconverting matrix between two SLOCC equivalent entangled states, and classification examples for some $$2\times 4\times M\times N$$2×4×M×N systems are also presented.