Necessary detection efficiencies for secure quantum key distribution and bound randomness

In recent years, several hacking attacks have broken the security of quantum cryptography implementations by exploiting the presence of losses and the ability of the eavesdropper to tune detection efficiencies. We present a simple attack of this form that applies to any protocol in which the key is constructed from the results of untrusted measurements performed on particles coming from an insecure source or channel. Because of its generality, the attack applies to a large class of protocols, from standard prepare-and-measure to device-independent schemes. Our attack gives bounds on the critical detection efficiencies necessary for secure quantum key distribution, which show that the implementation of most partly device-independent solutions is, from the point of view of detection efficiency, almost as demanding as fully device-independent ones. We also show how our attack implies the existence of a form of bound randomness, namely nonlocal correlations in which a nonsignalling eavesdropper can find out a posteriori the result of any implemented measurement.