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

TL;DR

This paper demonstrates that local preservation of the no-signaling principle can occur in multiparty PT-symmetric evolutions with real eigenvalues, even when bipartite versions violate no-signaling, using conventional inner products.

Contribution

It shows that within the standard Dirac inner product formalism, certain multiparty PT-symmetric evolutions preserve no-signaling locally, a phenomenon not observed in bipartite cases.

Findings

GHZ states exhibit local no-signaling preservation

W states do not support local no-signaling preservation

Violation can be avoided without non-conventional inner products

Abstract

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.