Robustness of multipartite entanglement in W and Greenberger–Horne–Zeilinger mixed states

Abstract

Quantifying entanglement is an essential endeavor for both quantum foundations and quantum technologies. The robustness is one of the tractable measures for quantifying quantum resources. As many experiments aim at the generation of multipartite entanglement states, we propose a method of calculating the robustness of multipartite entanglement for Greenberger–Horne–Zeilinger (GHZ) and W mixed states. We analytically determine the upper and lower bounds of robustness for three-qubit GHZ and W mixed states, and derive a tractable solution of the robustness bounds for four-qubit GHZ and W mixed states. Our results show that the upper bound matches the lower bound well, which verifies the validity of our methods.