A source distributes noisy entangled pairs to two stations whose devices are not…
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 source distributes noisy entangled pairs to two stations whose devices are not trusted (device-independent QKD). CHSH tests on a subset of the pairs show the devices win the CHSH game with probability pwin=0.83.
((a)) Using the relation S=8(pwin−21) for the CHSH combination, compute S.
((b)) Convert S to an equivalent error rate for a pair mixed with white noise, Q=(1−S/(22))/2, and decide whether it beats the device-independent threshold S≈2.42 (Q≈7.1%).
((c)) Using the device-independent bound quoted for collective attacks, r≥1−h(Q)−h(21+(S/2)2−1), compute the asymptotic key rate these untrusted devices can certify, and compare it with the rate 1−2h(Q) that trusted devices would give at the same Q.
((d)) If the two stations were instead trusted and used the entanglement-based BB84 argument with a Calderbank-Shor-Steane (CSS) code to correct bit and phase errors at this Q, state in words the property the two classical linear codes C1, C2 making up the CSS code must have, and explain why the phase-correction step does not need to be carried out on any physical qubit.