Limitations on quantum key repeaters for all key correlated states

TL;DR

This paper establishes a new bound on quantum key repeater rates for all key correlated states, using relative entropy measures, which broadens understanding of quantum internet security and key distribution limits.

Contribution

It introduces a novel bound on quantum key repeater rates applicable to a wide class of states, avoiding NP-hard problems and generalizing previous bounds.

Findings

Bound exceeds twice the one-way distillable entanglement by at most the max relative entropy of entanglement.

The bound applies to a broader class of states than previous results.

Provides an upper limit on private randomness for a generic independent bit.

Abstract

Quantum key repeater is the backbone of the future Quantum Internet. It is an open problem to determine, for an arbitrary mixed bipartite state shared between the stations of a quantum key repeater, how much key can be generated between its two end-nodes. We place a novel bound on the quantum key repeater rate, which uses the relative entropy distance from, in general, entangled quantum states. It allows us to generalize bounds on key repeaters of M. Christandl and R. Ferrara [Phys. Rev. Lett. 119, 220506]. As in the latter article, we consider a scenario used for measurement-device-independent quantum cryptography. The derived bound, although not tighter, holds for a more general class of states, thereby avoiding the NP-hard separability problem. We show that the repeated key of the broad class of key correlated states can exceed twice the one-way distillable entanglement by at most the max relative entropy of entanglement of its attacked version. We also provide a non-trivial upper bound on the amount of private randomness of a generic independent bit - a state containing one bit of ideal private randomness.