A double selection entanglement distillation-based state estimator

With the advent of practical quantum communication networks drawing closer, there is a growing need for reliable estimation protocols that can efficiently characterize quantum resources with minimum resource overhead requirement. A novel approach to this problem is to integrate an estimator into an existing network task, thereby removing the need for an additional characterization protocol. In this work, we show that the measurement statistics of a double selection distillation protocol alone can be used to efficiently estimate the Bell-diagonal parameters of the undistilled states, as well as the resulting distilled states after additional post-processing. We also demonstrate that this novel estimator outperforms the previously proposed distillation-based estimator in terms of resource complexity.