Fidelity estimation via local measurements in the presence of arbitrarily correlated noise

Fidelity estimation for entangled states shared by remote nodes is an essential building block for the quality control in quantum networks. In the literature, the issue of minimizing the efficiency loss in fidelity estimation due to the limitation of local operations and the issue of characterizing the accuracy of fidelity estimation protocols in the presence of arbitrary noise remain interesting challenges. This work addresses these two challenges, designs a protocol for estimating the average fidelity of qubit pairs shared by remote agents, whose efficiency reaches the fundamental upper bound achievable with local operations, and characterizes the performance of the proposed protocol in the presence of arbitrary noise. Analysis has been performed to characterize which factors affect the estimation accuracy and how. Numerical tests have been performed to check the preciseness and robustness of the proposed protocol, as well as to characterize the proper parameter setting. The analysis and numerical tests have identified the distinctive factors that affect the estimation accuracy in the presence of arbitrary noise, and have given clear instructions on how to properly address these factors.