Quantum-enhanced rotation measurements – a multiparameter problem

Precise rotation measurements have numerous classical and quantum applications. Particular quantum states can be used to dramatically increase sensitivities in estimating rotation angles around a known axis. We present a class of states that offer similar enhanced sensitivities in estimating both the orientation of an unknown rotation axis and the angle rotated about it. We derive a quantum Cramér-Rao bound for simultaneously estimating the three Euler angles of a rotation and discuss states that achieve Heisenberg-limited sensitivities for all three. Our states are "anticoherent" states, for whose identification we provide new geometric insights. This result is immediately useful for shot-noise-limited metrology.

Journal reference: Physical Review A 98 (3), 032113