Quantum key distribution over quantum repeaters with encoding: Using Error Detection as an Effective Post-Selection Tool

We propose a post-selection technique, based on quantum error detection, for quantum key distribution (QKD) systems that run over quantum repeaters with encoding. In such repeaters, quantum error correction techniques are used for entanglement distillation. By developing an analytical approach to study such quantum repeaters, we show that, in the context of QKD, it is often more efficient to use the error detection, rather than the error correction, capability of the underlying code to sift out cases where an error has been detected. We implement our technique for three-qubit repetition codes by modelling different sources of error in crucial components of the system. We then investigate in detail the impact of such imperfections on the secret key generation rate of the QKD system, and how one can use the information obtained during entanglement swapping and decoding stages to maximize the rate. For benchmarking purposes, we specify the maximum allowed error rates in different components of the setup below which positive key rates can be obtained.