  Violation of the no-signaling principle may occur in PT-symmetric evolutions,
that is, evolutions that stem from Hamiltonians that are symmetric with respect
to parity and time-reversal, of bipartite entangled states. The violation can
be avoided by using a non-conventional inner product. We show that even within
the formalism that utilizes the conventional Dirac inner product between
physical state vectors, it is possible to obtain instances of local
preservation of the no-signaling principle for evolutions corresponding to
PT-symmetric non-hermitian Hamiltonians with real eigenvalues, of multiparty
entangled states, whose bipartite versions still violate the principle. The
phenomenon can be witnessed already by using the Greenberger-Horne-Zeilinger
state. Interestingly, the generalized W states do not support such a local
preservation of no-signaling.
