Bound entanglement maximally violating Bell inequalities: quantum   entanglement is not equivalent to quantum security
  It is shown that Smolin four-qubit bound entangled states [Phys. Rev. A, 63 032306 (2001)] can maximally violate two-setting Bell inequality similar to standard CHSH inequality. Surprisingly this entanglement does not allow for secure key distillation, so neither entanglement nor violation of Bell inequalities implies quantum security. It is also pointed out how that kind of bound entanglement can be useful in reducing communication complexity. 
Remigiusz Augusiak, Pawel Horodecki