Pre-Privacy Amplification: A Post-Processing Technique for Quantum Key Distribution with Application to the Simplified Trusted Relay

Abstract

Until quantum repeaters and quantum error correcting codes can be made commercially viable, long distance quantum key distribution (QKD) will continue to rely on trusted relay satellites. Strongly constrained by weight and power efficiency, little room is left for raw computational power, lowering the key rate per second. Efforts to reduce the computational burden on satellites, such as the simplified trusted relay (which does not participate in privacy amplification), come at a significant cost to their key rate per bit sent and maximum tolerable error rate. We construct a post processing technique, that acts as a sort of pre-privacy amplification that is performed before the usual error correction and privacy amplification steps. Loosely speaking, it provides a way to scale between the simplified trusted relay and the usual full trusted relay. For the asymptotic qubit six-state protocol, we demonstrate an increase in the maximum tolerable error rate from ∼12.62% to ∼12.83% for the full trusted relay, and from ∼9.05% to ∼11.7% for the simplified trusted relay. We also provide several sufficient conditions to determine when unique reduction matrices will yield identical key rates.