Coherence transfer in quantum networks

Detecting coherence transfer in complex quantum networks can be challenging due to uncharacterized experimental conditions and limited system access. Here, we use static and dynamic coherence features to introduce a nonlinear criterion for identifying coherence transfer. The criterion requires only two measurement settings for network-state populations in an experimental state basis, regardless of the network's size. It remains valid even when the verification capabilities of checkpoint nodes are uncharacterized. The principle and method are general, encompassing networks with different access levels and scenarios, from those requiring no input changes to those involving coherence dynamics in the time domain. Experimentally, using remote state preparation and entanglement swapping, we transfer single polarization qubits and polarization-entangled pairs in four- and six-photon entanglement networks. The criterion provides experimental evidence of coherence transfer in multi-photon entanglement networks. Our findings offer a practical tool for coherence transfer in quantum information and open quantum systems in networks.