Quantum Sensing: Limits and Resources

The problem of measuring a function of local fields, each coupled to a quantum sensor, is a useful test bed for understanding multiparameter quantum metrology, with applications ranging from gravimetry to magnetometry. The fact that we are interested in a single quantity means that we can derive performance bounds using techniques of single parameter quantum metrology, but the saturability of such bounds depends on a full accounting of the multiparameter nature of the problem. While techniques for non-interacting quantum sensor networks are well-understood, with known optimal protocols, the case of interacting qubits presents unresolved challenges. In this work, we study a class of interacting Hamiltonians that can be harnessed to enhance function estimation. We derive optimality conditions for estimating linear functions and demonstrate that the precision bounds can be saturated up to a constant factor. This method offers a pathway for improving global parameter estimation in interacting quantum sensor networks.