Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states
You Zhou
Abstract
Entanglement is an essential resource in many quantum information tasks and the entanglement witness is a widely used tool for its detection. In experiments the prepared state generally deviates from the target state due to some noise. Normally the white-noise model is applied to quantifying such a derivation and at the same time reveals the robustness of the witness. However, there may exist other kinds of noise, in which the coherent noise can dramatically ``rotate'' the prepared state. In this way, coherent noise is likely to lead to a failure of detection, even though the underlying state is actually entangled. In this work, we propose an efficient entanglement detection protocol for $N$-partite Greenberger-Horne-Zeilinger (GHZ)--like states. The protocol can eliminate the effect of coherent noise and at the same time feedback the corresponding noise parameters, which are beneficial to further improvements of the experiment system. In particular, we consider two experiment-relevant coherent noise models; one is from the unconscious phase accumulation on $N$ qubits, and the other is from the rotation on the control qubit. The protocol effectively realizes a family of entanglement witnesses by postprocessing the measurement results from $N+2$ local measurement settings, which adds only one more setting than the original witness specialized for the GHZ state. Moreover, by considering the trade-off between the detection efficiency and the white-noise robustness, we further reduce the number of local measurements to three without altering the performance under the coherent noise. Our protocol can enhance entanglement detection under coherent noises and act as a benchmark for state-of-the-art quantum devices.