Local preservation of no-signaling in multiparty PT-symmetric evolutions

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.