  Periodically modulated nonlinear oscillators often display bistability of
forced vibrations. This bistability can be used for new types of quantum
measurements. They are based on switching between coexisting vibrational
states. Since switching is accompanied by a large change of the amplitude and
phase of forced vibrations, the measurements are highly sensitive. Quantum and
classical noise plays dual role. It imposes a limitation on sensitivity in the
familiar regime of a bifurcation amplifier. On the other hand, it makes it
possible to use a bistable modulated oscillator in a new regime of a balanced
dynamical bridge. We discuss the switching probabilities and show that they
display scaling with control parameters. The critical exponents are found for
different types of bifurcations and for different types of noise.
