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

Abstract

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.