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Fidelity estimation is essential for the quality control of entanglementdistribution networks. Because measurements collapse quantum states, weconsider a setup in which nodes randomly sample a subset of the entangled qubitpairs to measure and then estimate the average fidelity of the unsampled pairsconditioned on the measurement outcome. The proposed estimation protocolachieves the lowest mean squared estimation error in a difficult scenario witharbitrary noise and no prior information. Moreover, this protocol isimplementation friendly because it only performs local Pauli operatorsaccording to a predefined sequence. Numerical studies show that compared toexisting fidelity estimation protocols, the proposed protocol reduces theestimation error in both scenarios with i.i.d. noise and correlated noise.

Minimization of the estimation error for entanglement distribution networks with arbitrary noise