Private states, quantum data hiding and the swapping of perfect secrecy

TL;DR

This paper explores the relationship between quantum data hiding and privacy, introduces simplified private states, bounds their entanglement distillation, and discusses extending quantum key distribution via quantum repeaters.

Contribution

It establishes a formal connection between data hiding and privacy, simplifies private states, and analyzes the limits of quantum key distribution extension using entanglement swapping.

Findings

Bound on one-way distillable entanglement of private states.

Protocols for key distillation relate to data hiding states.

Entanglement swapping is optimal for extending quantum secrecy.

Abstract

We derive a formal connection between quantum data hiding and quantum privacy, confirming the intuition behind the construction of bound entangled states from which secret bits can be extracted. We present three main results. First, we show how to simplify the class of private states and related states via reversible local operation and one-way communication. Second, we obtain a bound on the one-way distillable entanglement of private states in terms of restricted relative entropy measures, which is tight in many cases and shows that protocols for one-way distillation of key out of states with low distillable entanglement lead to the distillation of data hiding states. Third, we consider the problem of extending the distance of quantum key distribution with help of intermediate stations. In analogy to the quantum repeater, this paradigm has been called the quantum key repeater. We show that when extending private states with one-way communication, the resulting rate is bounded by the one-way distillable entanglement. In order to swap perfect secrecy it is thus essentially optimal to use entanglement swapping.