  Quantum sensing is one of the key areas which exemplifies the superiority of
quantum technologies. Nonetheless, most quantum sensing protocols operate
efficiently only when the unknown parameters vary within a very narrow region,
i.e., local sensing. Here, we provide a systematic formulation for quantifying
the precision of a probe for multi-parameter global sensing when there is no
prior information about the parameters. In many-body probes, in which extra
tunable parameters exist, our protocol can tune the performance for harnessing
the quantum criticality over arbitrarily large sensing intervals. For the
single-parameter sensing, our protocol optimizes a control field such that an
Ising probe is tuned to always operate around its criticality. This
significantly enhances the performance of the probe even when the interval of
interest is so large that the precision is bounded by the standard limit. For
the multi-parameter case, our protocol optimizes the control fields such that
the probe operates at the most efficient point along its critical line.
Interestingly, for an Ising probe, it is predominantly determined by the
longitudinal field. Finally, we show that even a simple magnetization
measurement significantly benefits from our optimization and moderately
delivers the theoretical precision.
