The maximal violation of the Svetlichny inequality for “X” states and the extended GHZ states

Abstract

For a quantum system, violation of a Svetlichny inequality indicates the existence of genuine nonlocality. Through the same mathematical analysis approach, we derive the analytical expressions of the maximal violation of the Svetlichny inequality for certain three-qubit pure states and mixed “X” states. These pure states represented in the five-parameter form belong to extended GHZ states. It is convenient to use the obtained expression to distinguish the genuine nonlocal states in these states. We also obtain the analytical expression of the maximal violation of Svetlichny inequality for a subclass of four-qubit “X” states. We show the application potentiality of these expressions by designing two schemes where quantum resources are converted from less qubits “X” states to more qubits “X” states.