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.

• Received 15 January 2007

DOI:https://doi.org/10.1103/PhysRevA.75.032306