A Research On Classifications For Multipartite Entangled Quantum States

In the paper, we discuss two kinds of classifications for multipartite entangled quantum states, called LU equivalence and SLOCC equivalence. The former is discussed by high-order singular value decomposition technique, multidimensional tensor respective matrix representations and local symmetries of the states. Two states are LU equivalent if and only if their core tensors are related by some certain operators. The latter also studies multidimensional tensors’respective matrix rep-resentations and how multipartite quantum states are transformed into matrixes. By the different determinants and ranks, we discuss the properties of the equiva-lence under SLOCC. We get that two pure states in a bipartite system are SLOCC equivalent if and only if their Schmidt numbers are the same. At last, we give some examples about SLOCC equivalence.