Figure 4: Dependence of phase error on repeat number and input phases.

(a) Standard deviations of the entangled state and independent state against repeat number. Single-spin states (electron and nuclear) of the same input phase ϕ=30° are prepared and measured independently, the phase extracted from each entangled state ‘single measurement’ is 2ϕ=60°. (b) The phase uncertainty is fitted by function for both single-spin state and the entangled state, where v corresponds to repeat number in unit of million (M). The curves show that the phase uncertainty, phase error represented by δϕ, of entanglement case is apparently lower than the case of single-spin state. (c) The phase estimation results of different input phases including 0°, 5°, 10°, 15°, 20°, 25° and 30°, the repeat number is fixed to 1 M. (d) The phase error of different input phases, the repeat number is fixed to 1 M.