Sequential weak measurements followed by a final projective measurement extend the dynamic range of coherent-spin-state frequency estimation and asymptotically saturate the noiseless quantum Fisher information bound.
However, for pe ̸= 1, the sensing qubit becomes a mixed state due to imperfect measurements, and r undergoes a stochastic process (in addition to ϕ)
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Extending the dynamic range in quantum frequency estimation with sequential weak measurements
Sequential weak measurements followed by a final projective measurement extend the dynamic range of coherent-spin-state frequency estimation and asymptotically saturate the noiseless quantum Fisher information bound.