Irreducible private states
Karol Horodecki, Piotr Ćwikliński, Adam J. Rutkowski, Michał Studziński · arXiv (Cornell University) · 2016
Hereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We prove also a tighter upper bound on its performance. This implies in particular that the irreducible private states are all strictly irreducible if and only if the entangled but key-undistillable states (bound key states) exist. In turn, all the irreducible private states of the dimension $4\otimes 4$ are strictly irreducible, that is, after an attack on the key part they become separable states. Providing the bound key states exist, we consider different subclasses of the irreducible private states and their properties. Finally we show a possible way to apply our findings in the context of quantum key repeaters. As a step towards this direction, we provide a lower bound on the trace norm distance between key-undistillable states and private states, in sufficiently high dimensions, yet not large enough to reach the goal of application. However this bound leads to the proof of no-key swapping for some private states in the single copy case without using the fact that they are strictly irreducible.