Nonlocality and efficiency of three-qubit partially entangled states

We analyse nonlocal properties in three-qubit partially entangled W-n states to understand the efficiency of these states as entangled resources. Our results show that W-n states always violate the three-qubit Svetlichny inequality, and the degree of violation increases with the increase in degree of entanglement. We find that nonlocal correlations in W-1 states are the highest in comparison to all other W-n states. We further demonstrate that within the limits of experimentally achievable measurements the W-1 state proves to be a better quantum resource for specific protocols in comparison to standard W states, even though the degree of entanglement and nonlocality in the W-1 state are less than the degree of entanglement and nonlocality in the standard W state. Moreover, we also consider superpositions of the Greenberger-Horne-Zeilinger (GHZ) state with W and W-1 states to show that more entanglement is not a necessity for better efficiency in all protocols. In addition, we also demonstrate the preparation of three qubit quantum states represented as linear superpositions of the GHZ state with W and W-1 states.