Hybrid one-way quantum repeater concatenated with the [[5,1,3]] code

Abstract

An improvement to the existing one-way quantum repeater network using the tree cluster state as the quantum error correcting code is presented. Namely, the [[5,1,3]] quantum error correcting code is introduced as an outer code while the tree code becomes the inner code. Using this approach, we present a novel hybrid one-way quantum repeater architecture with more than one type of quantum repeater in its network. We considered both the non-fault-tolerant and fault-tolerant variants of the [[5,1,3]] code in our study of the hybrid repeater network. A novel improvement to the [[5,1,3]] code is also presented, where we also consider using it for quantum erasure correction. Additionally, we introduced a novel method of extrapolating an approximate fidelity of a quantum state after arbitrary applications of a noisy quantum channel. With these, we see magnitudes of order of boost in the resulting secret key rate in our approach.