Robustness of entanglement

Abstract

In the quest of completely describing entanglement in the general case of a finite number of parties sharing a physical system of finite dimensional Hilbert space a new entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurence of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of binary systems, and analytical bounds for mixed states of binary systems. Specific results are obtained mainly for the qubit-qubit system. As byproducts local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced and arguments for considering convexity a necessary condition of any entanglement magnitude are put forward.