Symmetry Transformations on the Set of Tensor Products of Rank-1 Idempotents

We obtain a characterization of bijective maps preserving the trace of products on the set of tensor products of rank-1 idempotents, which may be considered as a generalization of Molnár’s Wigner-type theorem in multipartite systems. The proof is based on the studies in linear preserver problems on tensor products. Moreover, a corresponding result on the finite-dimensional case is presented.