**Bound entangled states and distillable key rate** - Jeongsan Kim

In this talk, we consider some sufficient conditions for quantum states to have positive distillable key rate [Phys. Rev. .A 75, 032306(2007)]. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005), quant-ph/0506203] 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 distillable key rate for the 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. We will also consider the geometric distance and its lower bound of PPT bound entangled state from the set of private states for a fixed dimension.