Detection of arbitrary quantum correlations via synthesized quantum channels

Quantum correlations are key information about the structures and dynamics of quantum many-body systems. There are many types of high-order quantum correlations with different time orderings, but only a few of them are accessible to the existing detection methods. Recently, a quantum-sensing approach based on sequential weak measurement was proposed to selectively extract arbitrary types of correlations. However, its experimental implementation is still elusive. Here we demonstrate the extraction of arbitrary types of quantum correlations. We generalized the original weak measurement scheme to a protocol using synthesized quantum channels, which can be applied to more universal scenarios including both single and ensemble quantum systems. In this quantum channel method, various controls on the sensors are superimposed to select the sensor-target evolution along a specific path for measuring a desired quantum correlation. Using the versatility of nuclear magnetic resonance techniques, we successfully extract the second- and fourth-order correlations of a nuclear-spin target by another nuclear-spin sensor. The full characterization of quantum correlations provides a new tool for understanding quantum many-body systems, exploring fundamental quantum physics, and developing quantum technologies.