Private States, Quantum Data Hiding, and the Swapping of Perfect Secrecy

An important contribution to the understanding of quantum key distribution has been the discovery of
entangled states from which secret bits, but no maximally entangled states, can be extracted [Horodecki
et al., Phys. Rev. Lett. 94, 200501 (2005)]. The construction of those states was based on an intuition that
the quantum mechanical phenomena of data hiding and privacy might be related. In this Letter we firmly
connect these two phenomena and highlight three aspects of this result. First, we simplify the definition of
the secret key rate. Second, we give a formula for the one-way distillable entanglement of certain private
states. Third, we consider the problem of extending the distance of quantum key distribution with help of
intermediate stations, a setting called the quantum key repeater. We show that for protocols that first distill
private states, it is essentially optimal to use the standard quantum repeater protocol based on entanglement
distillation and entanglement swapping.