  Quantum sensing is one of the arenas that exemplifies the superiority of
quantum technologies over their classical counterparts. Such superiority,
however, can be diminished due to unavoidable noise and decoherence of the
probe. Thus, metrological strategies to fight against or profit from
decoherence are highly desirable. This is the case of certain types of
decoherence-driven many-body systems supporting dissipative phase transitions,
which might be helpful for sensing. Boundary time crystals are exotic
dissipative phases of matter in which the time-translational symmetry is
broken, and long-lasting oscillations emerge in open quantum systems at the
thermodynamic limit. We show that the transition from a symmetry unbroken into
a boundary time crystal phase, described by a second-order transition, reveals
quantum-enhanced sensitivity quantified through quantum Fisher information. We
also determine the critical exponents of the system and establish their
relationship. Our scheme is indeed a demonstration of harnessing decoherence
for achieving quantum-enhanced sensitivity. From a practical perspective, it
has the advantage of being independent of initialization and can be captured by
a simple measurement.
