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Entanglement is an essential resource in many quantum information tasks andentanglement witness is a widely used tool for its detection. In experimentsthe prepared state generally deviates from the target state due to some noise.Normally the white noise model is applied to quantifying such derivation and inthe same time reveals the robustness of the witness. However, there may existother kind of noise, in which the coherent noise can dramatically "rotate" theprepared state. In this way, the coherent noise is likely to lead to a failureof the detection, even though the underlying state is actually entangled. Inthis work, we propose an efficient entanglement detection protocol for$N$-partite Greenberger-Horne-Zeilinger (GHZ)-like states. The protocol caneliminate the effect of the coherent noise and in the same time feedback thecorresponding noise parameters, which are beneficial to further improvements onthe experiment system. In particular, we consider two experiment-relevantcoherent noise models, one is from the unconscious phase accumulation on $N$qubits, the other is from the rotation on the control qubit. The protocoleffectively realizes a family of entanglement witnesses by postprocessing themeasurement results from $N+2$ local measurement settings, which only adds onemore setting than the original witness specialized for the GHZ state. Moreover,by considering the trade-off between the detection efficiency and thewhite-noise robustness, we further reduce the number of local measurements to 3without altering the performance on the coherent noise. Our protocol canenhance the entanglement detection under coherent noises and act as a benchmarkfor the state-of-the-art quantum devices.

Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states