Transformation of a class of pure multipartite entangled states

Entanglement transformation can give insight into quantum entanglement and provide desired resources for quantum information processing. However, the complexity for analyzing entanglement transformation exponentially grows with the increased particle numbers. We find that a sort of multipartite entangled states can be described by the Valence-bond state (VBS) picture and can be decomposed into a series of cells. Thus the study of multipartite entanglement can be greatly simplified. We propose an inverse entanglement resource searching method by which one can find states that can be transformed into desired entangled resource states via local operations and classical communication (LOCC) and stochastic LOCC (SLOCC). In the case of bipartite entanglement, our method includes Nielsen’s majorization theorem as a special case. We apply the method to measurement based quantum computation (MBQC) and find some resource states for MBQC that can be transformed into Cluster states via LOCC or SLOCC. We also construct the Hamiltonians of two-body nearest neighbor interactions with the found resource states as their eigenstates.