  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.
