Correlation spectroscopy with a network of quantum sensors

We consider a network of quantum sensors, consisting of N qubits, with strong correlated dephasing. While every single sensor is completely incoherent, the correlations in the noise allow to sense multi-particle properties such as phase differences. We generalize the notion of correlation spectroscopy for estimation of all phase differences in this network. This method, which involves all N -particle correlations, reduces the measurement uncertainty as compared to the traditional method where only two-particle correlations are analyzed.

Quantum precision limits and optimal sensing techniques for this problem are derived: for any finite N the optimal initial states are entangled states but in the limit of large N our entanglement-free correlation spectroscopy is asymptotically optimal. 

We use this generalized correlation spectroscopy for measuring ion-ion distances and transition frequency shifts in one- and two-dimensional ion crystals by analyzing multi-particle correlations of up to N = 91 qubits, each of which is encoded in a single ion.