(color online) Entanglement-enhanced phase estimation. (a) Phase estimation schemes of the independent states and the electron-nuclear entangled state. By harnessing entanglement, quantum metrology yields higher statistical precision than classical approaches. (b) Phase relation of an independent states and entangled states. (c) The phase uncertainty is fitted by function for both single spin state and the entangled state, where ν corresponds to repeat number in unit of million (M). The curves show that the phase uncertainty, phase error represented by , of entanglement case is apparently lower than the case of single spin state. (d) The phase error of different input phases, the repeat number is fixed to 1 M. Reproduced from Ref. [87], NPG.