  We introduce the concept of a superlinear threshold detector, a detector that
has a higher probability to detect multiple photons if it receives them
simultaneously rather than at separate times. Highly superlinear threshold
detectors in quantum key distribution systems allow eavesdropping the full
secret key without being revealed. Here, we generalize the detector control
attack, and analyze how it performs against quantum key distribution systems
with moderately superlinear detectors. We quantify the superlinearity in
superconducting single-photon detectors based on earlier published data, and
gated avalanche photodiode detectors based on our own measurements. The
analysis shows that quantum key distribution systems using detector(s) of
either type can be vulnerable to eavesdropping. The avalanche photodiode
detector becomes superlinear towards the end of the gate, allowing
eavesdropping using trigger pulses containing less than 120 photons per pulse.
Such an attack would be virtually impossible to catch with an optical power
meter at the receiver entrance.
