Saturable global quantum sensing

Conventional formulation of quantum sensing has been mostly developed in the context of local estimation, where the unknown parameter is roughly known. In contrast, global sensing, where the prior information is incomplete and the unknown parameter is only known to lie within a broad interval, is practically more engaging but has received far less theoretical attention. Available formulations of global sensing rely on adaptive Bayesian strategies requiring on-the-fly change in measurement settings, or minimizing average uncertainty yielding unsaturable bounds. Here, we provide an operationally motivated approach to global sensing for fixed but optimized settings. Our scheme yields a saturable precision bound optimizing the measurement as well as the probe preparation simultaneously. The formalism is general and computationally scalable for generic bosonic multimode Gaussian or many-particle free-fermionic quantum sensors. We illustrate the implications for Gaussian thermometry and Gaussian phase estimation by showing that the optimal measurement changes, either gradually or abruptly, from homodyne for local sensing, towards heterodyne for global sensing. In contrast, for fermionic transverse XY probes, the optimal measurement basis stays fixed independent of width.