Local preservation of no-signaling in multiparty <i>PT</i>-symmetric evolutions

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