A vendor's technical note claims: 'Standard telecom fibre links use inline…
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum information theory and communication · Quantum information theory and communication
Quantum Information and Technology, Ch Quantum key distribution and quantum networks
Problem
A vendor's technical note claims: 'Standard telecom fibre links use inline erbium-doped optical amplifiers roughly every 80km to restore signal power. We do the same for our QKD system: an amplifier every 60km restores the pulse to its original mean photon number, so a 120km link performs exactly as well as a 60km link and easily beats the repeaterless bound.'
((a)) Explain, using the no-cloning theorem, why no physical amplifier can restore an intercepted BB84 signal photon's unknown polarisation state without either failing part of the time or adding noise that raises the error rate, and say what this means for the vendor's claim.
((b)) The fibre used has attenuation 0.20dBkm−1. Compute the transmission ηseg of one 60km segment and the direct end-to-end transmission ηdirect over the full 120km. Compare ηdirect with ηseg2.
((c)) A genuine repeater instead places a quantum memory at the midpoint and attempts entanglement generation on each 60km segment independently, holding a successful segment in memory until its partner succeeds too, and only then swapping. Explain why the rate of producing an end-to-end pair with this scheme scales as ηseg rather than ηseg2. Then, treating attempts as synchronous rounds in which each segment succeeds independently with probability ηseg, and the memory as perfect, compute the expected number of rounds until both segments have succeeded, and the resulting factor of improvement over a one-shot attempt that needs both segments to succeed in the same round.