Upper Bounds on Device-Independent Quantum Key Distribution Rates and a Revised Peres Conjecture

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