Asymptotic relation between Bell-inequality violations and entanglement distillability

We investigate the asymptotic relation between violations of the Mermin-Belinskii-Klyshko inequality and the entanglement distillability of multipartite entangled states, as the number of parties increases. We in particular consider noisy multiqubit GHZ and so-called Dur states in the Mermin-Belinskii-Klyshko inequality, and show that, in the asymptotic limit of the number of parties, the violation of the inequality implies the distillability in almost all bipartitions.The author thanks Dr. Bae for his fruitful comments on the work and careful reading of the manuscript. The author also thanks the referee for bringing Refs. [6] and [7] to his attention. This work is supported by the Research Fund of Hanyang University (Grant No. HYU-2010-T) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. KRF2009-0077028)