Description
Many-body interactions can introduce entanglement between particles and hence are valuable resources for quantum information processing. After a brief introduction of quantum metrology, I will discuss a variational principle for controlling many-body quantum systems with restricted operations in the context of quantum sensing. We show that in a spin chain model containing three-body interactions, the Heisenberg scaling can be still achieved even if the control operations are restricted to one-body and two-body interactions, given an initial GHZ state can be prepared. When the GHZ state cannot be efficiently prepared in experiments, one may consider many-body sensing with separable initial states. We find that using separable initial states cannot beat the shot noise limit in locally interacting systems, unless long-range non-local interactions are utilized. These findings identify two important ingredients in many-body sensing: initial entanglement and long-range interactions.
