For Toeplitz families of quantum states with a flat prior, the optimal measurement is a covariant quantum-whitening projection, and it can beat time-domain quadrature for coherent-state frequency estimation below the classical SNR threshold.
Suppose that G(θ) =δ(θ)/δ(0)such that the states are all orthogo- nal, e.g
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Bayesian frequency estimation at the fundamental quantum limit
For Toeplitz families of quantum states with a flat prior, the optimal measurement is a covariant quantum-whitening projection, and it can beat time-domain quadrature for coherent-state frequency estimation below the classical SNR threshold.