Robustness of Λ-entanglement of multipartite states

By introducing the relative robustness of Lambda-entanglement of a multipartite state related to a Lambda-separable state, the robustness of Lambda-entanglement of a multipartite state is defined as the minimum of the relative robustness of Lambda-entanglement of a state related to all Lambda-separable states. It is proved that, as a function on the set of all quantum states of an n-partite system, robustness of Lambda-entanglement is nonnegative, lower semi-continuous, and convex, and it is zero if and only if the state is Lambda-separable. Thus, robustness of Lambda-entanglement not only quantifies the endurance of Lambda-entanglement of a state against linear noise, but also can be used to distinguish Lambda-separable states from Lambda-entangled states. Furthermore, influences of a quantum channel on robustness of Lambda-entanglement are discussed.