  We study the effects of Lorentz transformations on three-particle non-local
system states (GHZ and W) of spin 1/2 particles, using the Pauli spin operator
and a three-particle generalization of Bell's inequality, introduced by
Svetlichny. In our setup, the moving and laboratory frames used the (same) set
of measurement directions that maximally violate Svetlichny's inequality in the
laboratory frame. We also investigate the behavior of Mermin's and Collins'
inequalities. We find that, regardless of the particles' type of entanglement,
violation of Svetlichny's inequality in the moving frame is decreased by
increasing the boost velocity and the energy of particles in the laboratory
frame. In the relativistic regime Svetlichny's inequality is a good criterion
to investigate the non-locality of the GHZ state. We also find that Mermin's
and Collins' inequalities lead to reasonable predictions, in agreement with the
behavior of the spin state, about non-locality of the W state in the
relativistic regime. Then, comparing our results with those in which Czachor's
relativistic spin is used instead of the Pauli operator, we find that the
results obtained by considering the Pauli spin operator are in better agreement
with the behavior of spin state of the system in the relativistic information
theory.

Quantum Physics