  Conventional classical sensors are approaching their maximum sensitivity
levels in many areas. Yet these levels still are far from the ultimate limits
dictated by quantum mechanics. Quantum sensors promise a substantial step ahead
by taking advantage of the salient sensitivity of quantum states to the
environment. Here, we focus on sensing rotations, a topic of broad application.
By resorting to the basic tools of estimation theory, we derive states that
achieve the ultimate sensitivities in estimating both the orientation of an
unknown rotation axis and the angle rotated about it. The critical enhancement
obtained with these optimal states should make of them an indispensable
ingredient in the next generation of rotation sensors that is now blossoming.
