title: Secure key from bound entanglement.
abstract: We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.
authors.affiliation: Department of Mathematics, Physics and Computer Science, University of Gdańsk, Poland.
authors.forename: Karol
authors.initials: K
authors.lastname: Horodecki
authors.forename: Michał
authors.initials: M
authors.lastname: Horodecki
authors.forename: Paweł
authors.initials: P
authors.lastname: Horodecki
authors.forename: Jonathan
authors.initials: J
authors.lastname: Oppenheim