A start-up markets an entanglement-based 'device-independent QKD' system for fibre links
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum states, measurement and entanglement · Quantum information theory and communication
Quantum Information and Technology, Ch Quantum key distribution and quantum networks
Problem
A start-up markets an entanglement-based 'device-independent QKD' system for fibre links. Its data sheet states three things: the photon-pair source is pumped so that the mean number of entangled pairs generated per pulse is μ=0.8; the source is 'inherently single-pair' and therefore not vulnerable to any multi-photon attack; and a bench test gave a CHSH game win rate of 78%, which the data sheet says 'certifies a device-independent secure key at the rate we quote.'
((a)) Treating the pair number per pulse as Poisson-distributed with mean μ=0.8, compute the fraction of non-empty pulses that in fact contain two or more pairs. Comment on the 'inherently single-pair' claim.
((b)) Convert the quoted win rate to the CHSH value S, and, using Q=(1−22S)/2 for pairs degraded by white noise, to an implied error rate Q.
((c)) The device-independent bound quoted for collective attacks becomes positive, for pairs mixed with white noise, only once S≳2.42 (equivalently a win rate ≳80%, Q≲7.1%). Decide whether the vendor's own bench figure supports the device-independent security claim, and say what, if anything, the 78% win rate does certify.