  This paper studies quantum limits to dynamical sensors in the presence of
decoherence. A modified purification approach is used to obtain tighter quantum
detection and estimation error bounds for optical phase sensing and
optomechanical force sensing. When optical loss is present, these bounds are
found to obey shot-noise scalings for arbitrary quantum states of light under
certain realistic conditions, thus ruling out the possibility of asymptotic
Heisenberg error scalings with respect to the average photon flux under those
conditions. The proposed bounds are expected to be approachable using current
quantum optics technology.
