  The problem of continuous quantum measurement of coherent oscillations in an
individual quantum two-state system is studied for a generic model of the
measuring device. It is shown that for a symmetric detector, the
signal-to-noise ratio of the measurement, defined as the ratio of the amplitude
of the oscillation line in the output spectrum to background noise, is
independent of the coupling strength between oscillations and the detector, and
is equal to $(\hbar/\epsilon)^2$, where $\epsilon$ is the detector energy
sensitivity. The fundamental quantum limit of 4 imposed by this result on the
signal-to-noise ratio of the measurement with an ``ideal'' quantum-limited
detector reflects the general tendency of a quantum measurement to localize the
system in one of the eigenstates of the measured observable. These results are
applied to specific measurements of the quantum oscillations of magnetic flux
with a dc SQUID, and oscillations of charge measured with a Cooper-pair
electrometer. They are also used to calculate the energy sensitivity of a
quantum point contact as detector.
