Optimal and Secure Measurement Protocols for Quantum Sensor Networks
  Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound. 
Zachary Eldredge, Michael Foss-Feig, Jonathan A. Gross, Steven L.   Rolston, Alexey V. Gorshkov
quant-ph