Bound entangled states with a nonzero distillable key rate

We present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005)] have nonzero distillable key rate and finally exhibit new classes of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of the distillable key rate for the classical-classical-quantum (ccq) states of their privacy squeezed versions, which represent the states after the local measurement performed in the key part without considering the shield part.