  Precisely measuring the three-dimensional position and orientation of
individual fluorophores is challenging due to the substantial photon shot noise
in single-molecule experiments. Facing this limited photon budget, numerous
techniques have been developed to encode 2D and 3D position and 2D and 3D
orientation information into fluorescence images. In this work, we adapt
classical and quantum estimation theory and propose a mathematical framework to
derive the best possible precision for measuring the position and orientation
of dipole-like emitters for any fixed imaging system. We find that it is
impossible to design an instrument that achieves the maximum sensitivity limit
for measuring all possible rotational motions. Further, our vectorial dipole
imaging model shows that the best quantum-limited localization precision is
~4-8% worse than that suggested by a scalar monopole model. Overall, we
conclude that no single instrument can be optimized for maximum precision
across all possible 2D and 3D localization and orientation measurement tasks.
