Improving entanglement resilience in quantum memories with error-detection-based distillation

The degradation of entanglement in quantum memories due to decoherence is a critical challenge for scalable quantum networks. We present an entanglement distillation protocol based on the [[4, 2, 2]] quantum error-detecting code, deriving analytical expressions for its output fidelity and yield, and benchmarking it against the BBPSSW protocol. In addition to single-round performance, we further examine the iterative behavior of both protocols through multi-round fidelity and cumulative yield analysis. We then investigate a storage-stage recovery strategy in which the retained logical entangled state is subjected to repeated stabilizer-based syndrome checks without decoding and re-encoding, avoiding the need to regenerate and redistribute entanglement from scratch. Our analysis shows that this strategy can extend the usable storage lifetime beyond the BBPSSW baseline when the classical communication latency is sufficiently small. We derive latency thresholds and quantify the cumulative acceptance probabilities for different numbers of syndrome checks. A sensitivity analysis further shows that local gate and measurement errors reduce the fidelity advantage region and the admissible communication latency window, highlighting the importance of sufficiently accurate local operations. These results provide a quantitative framework for assessing the storage-stage benefit of logical state retention in the presence of finite communication latency and nonideal local operations.