  Ever since the inception of gravitational-wave detectors, limits imposed by
quantum mechanics to the detection of time-varying signals have been a subject
of intense research and debate. Drawing insights from quantum information
theory, quantum detection theory, and quantum measurement theory, here we prove
lower error bounds for waveform detection via a quantum system, settling the
long-standing problem. In the case of optomechanical force detection, we derive
analytic expressions for the bounds in some cases of interest and discuss how
the limits can be approached using quantum control techniques.
