Asymptotically optimal joint phase and dephasing strength estimation using spin-squeezed states

We show an explicit $N$-qubit protocol involving one-axis-twisted spin squeezed states, that allows for simultaneous phase and dephasing strength estimation with precision that asymptotically matches fundamental quantum metrological bounds. The relevance of the protocol goes beyond this particular model, since any uncorrelated noise quantum metrological model, that allows for at most constant asymptotic quantum enhancement, can be reduced to this problem via an appropriately tailored quantum error-correction procedure.