Here we explore the possibility of precise time-keeping in quantum systems
using athermal resources. We show that quantum measurement engineered
reservoirs can be used as athermal resources to drive the ticks of a quantum
clock. Two and three level quantum systems act as transducers in our model,
converting the quantum measurement induced noise to produce a series of ticks.
The ticking rate of the clock is maximized when the measured observable
maximally non-commutes with the clock’s Hamiltonian. We use the large deviation
principle to characterize the statistics of observed ticks within a given
time-period and show that it can be sub-Poissonian — quantified by Mandel’s Q
parameter — alluding to the quantum nature of the clock. We discuss the
accuracy and efficiency of the clock, and extend our framework to include
hybrid quantum clocks fueled by both measurements, and thermal resources. We
make comparisons to relatable recent proposals for quantum clocks, and discuss
alternate device implementations harvesting the quantum measurement engineered
non-equilibrium conditions, beyond the clock realization.

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