Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture

TL;DR

This paper establishes upper bounds on the key rates for device-independent quantum key distribution protocols based on Bell inequality violations and introduces a revised Peres conjecture suggesting bound entangled states cannot be used for DIQKD, supported by initial evidence.

Contribution

It derives improved upper bounds on DIQKD key rates and proposes a revised Peres conjecture about the limitations of bound entangled states in DIQKD.

Findings

Upper bounds on DIQKD key rates based on Bell violation are tighter than previous bounds.

Bound entangled states cannot be used to generate keys in DIQKD protocols.

Evidence suggests bound entangled states cannot serve as resources for DIQKD.

Abstract

Device-independent quantum key distribution (DIQKD) is one of the most challenging tasks in quantum cryptography. The protocols and their security are based on the existence of Bell inequalities and the ability to violate them by measuring entangled states. We study the entanglement needed for DIQKD protocols in two different ways. Our first contribution is the derivation of upper bounds on the key rates of CHSH-based DIQKD protocols in terms of the violation of the inequality; this sets an upper limit on the possible DI key extraction rate from states with a given violation. Our upper bound improves on the previously known bound of Kaur et al. Our second contribution is the initiation of the study of the role of bound entangled states in DIQKD. We present a revised Peres conjecture stating that such states cannot be used as a resource for DIQKD. We give a first piece of evidence for the conjecture by showing that the bound entangled state found by Vertesi and Brunner, even though it can certify DI randomness, cannot be used to produce a key using protocols analogous to the well-studied CHSH-based DIQKD protocol.