  Many protocols require precise rotation measurement. Here we present a
general class of states that surpass the shot noise limit for measuring
rotation around arbitrary axes. We then derive a quantum Cram\'er-Rao bound for
simultaneously estimating all three parameters of a rotation (e.g., the Euler
angles), and discuss states that achieve Heisenberg-limited sensitivities for
all parameters; the bound is saturated by "anticoherent" states [Zimba,
Electron. J. Theor. Phys. 3, 143 (2006)] (we are reluctant to use
"anticoherent" to describe the states, but the name has become commonplace over
the last decade). Anticoherent states have garnered much attention in recent
years, and we elucidate a geometrical technique for finding new examples of
such states. Finally, we discuss the potential for divergences in
multiparameter estimation due to singularities in spherical coordinate systems.
Our results are useful for a variety of quantum metrology and quantum
communication applications.
