Abstract:

We considered influences of quantum channels on robustness of multi\|body entanglement. Firstly, we proved that the infimum in the definition of the robustness of entanglement (RoE) could be attained based on the fact that the set of all separable states was a convex closed set. Secondly, we proved that a convex combination of two different optimal states of the same entanglement state ρ was still the optimal state, and the RoE was a lower semicontinuous function on the set of all quantum states. Finally, we gave  necessary and sufficient conditions for the RoE of a quantum channel, which did not increase, did not reduce and maintained all quantum states.

Key words:  entanglement state, separable state, relative robustness of entanglement, robustness of entanglement, quantum channel