  Fidelity estimation is essential for the quality control of entanglement
distribution networks. Because measurements collapse quantum states, we
consider a setup in which nodes randomly sample a subset of the entangled qubit
pairs to measure and then estimate the average fidelity of the unsampled pairs
conditioned on the measurement outcome. The proposed estimation protocol
achieves the lowest mean squared estimation error in a difficult scenario with
arbitrary noise and no prior information. Moreover, this protocol is
implementation friendly because it only performs local Pauli operators
according to a predefined sequence. Numerical studies show that compared to
existing fidelity estimation protocols, the proposed protocol reduces the
estimation error in both scenarios with i.i.d. noise and correlated noise.
