  By carrying out measurements on entangled states, two parties can generate a
secret key which is secure not only against an eavesdropper bound by the laws
of quantum mechanics, but also against a hypothetical "post-quantum"
eavesdroppers limited by the no-signalling principle only. We introduce a
family of quantum key distribution protocols of this type, which are more
efficient than previous ones, both in terms of key rate and noise resistance.
Interestingly, the best protocols involve large number of measurements. We show
that in the absence of noise, these protocols can yield one secret bit per
entanglement bit, implying that the key rates in the no-signalling post-quantum
scenario are comparable to the key rates in usual quantum key distribution.
