Quantum states representing perfectly secure bits are always distillable
Paweł Horodecki, Remigiusz Augusiak · Physical Review A · 2006
It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension generalizations always represent distillable entanglement. The corresponding lower bounds on distillable entanglement are provided. We also present a simple alternative proof that for any bipartite quantum state entanglement cost is an upper bound on a distillable cryptographic key in a bipartite scenario.