  Small perturbations to systems near critical points of quantum phase
transitions can induce drastic changes in the system properties. Here I show
that this sensitivity can be exploited for weak-signal detection applications.
This is done by relating a widely studied signature of quantum chaos and
quantum phase transitions known as the Loschmidt echo to the minimum error
probability for a quantum detector and noting that the echo, and therefore the
error, can be significantly reduced near a critical point. Three examples,
namely, the quantum Ising model, the optical parametric oscillator model, and
the Dicke model, are presented to illustrate the concept. For the latter two
examples, the detectable perturbation can exhibit a Heisenberg scaling with
respect to the number of detectors, even though the detectors are not entangled
and no special quantum state preparation is specified.
