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Transformations involving only local operations assisted with classicalcommunication are investigated for multipartite entangled pure states havingtensor rank 2. All necessary and sufficient conditions for the possibility ofdeterministically converting truly multipartite, rank-2 states into each otherare given. Furthermore, a chain of local operations that successfully achievesthe transformation has been identified for all allowed transformations. Theidentified chains have two nice features: (1) each party needs to carry out atmost one local operation and (2) all of these local operations are alsodeterministic transformations by themselves. Finally, it is found that thereare disjoint classes of states, all of which can be identified by a single realparameter, which remain invariant under deterministic transformations.

Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2