  A boundary time-crystal is a quantum many-body system whose dynamics is
governed by the competition between coherent driving and collective
dissipation. It is composed of N two-level systems and features a transition
between a stationary phase and an oscillatory one. The fact that the system is
open allows to continuously monitor its quantum trajectories and to analyze
their dependence on parameter changes. This enables the realization of a
sensing device whose performance we investigate as a function of the monitoring
time T and of the system size N. We find that the best achievable sensitivity
is proportional to $\sqrt{T}N$, i.e., it follows the standard quantum limit in
time and Heisenberg scaling in the particle number. This theoretical scaling
can be achieved in the oscillatory time-crystal phase and it is rooted in
emergent quantum correlations. The main challenge is, however, to tap this
capability in a measurement protocol that is experimentally feasible. We
demonstrate that the standard quantum limit can be surpassed by cascading two
time-crystals, where the quantum trajectories of one time-crystal are used as
input for the other one.
