  Quantum sensors have been shown to be superior to their classical
counterparts in terms of resource efficiency. Such sensors have traditionally
used the time evolution of special forms of initially entangled states,
adaptive measurement basis change, or the ground state of many-body systems
tuned to criticality. Here, we propose a different way of doing quantum sensing
which exploits the dynamics of a many-body system, initialized in a product
state, along with a sequence of projective measurements in a specific basis.
The procedure has multiple practical advantages as it: (i) enables remote
quantum sensing, protecting a sample from the potentially invasive readout
apparatus; and (ii) simplifies initialization by avoiding complex entangled or
critical ground states. From a fundamental perspective, it harnesses a resource
so far unexploited for sensing, namely, the residual information from the
unobserved part of the many-body system after the wave-function collapses
accompanying the measurements. By increasing the number of measurement
sequences, through the means of a Bayesian estimator, precision beyond the
standard limit, approaching the Heisenberg bound, is shown to be achievable.
