Optimal probe states for phase estimation under covariant measurements are given by the principal eigenvector of a Toeplitz matrix constructed from the cost function, achieving Heisenberg scaling for a specific cost.
Ziv-zakai error bounds for quantum parameter estimation,
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Optimal Probe State for Phase Estimation Under Covariant Measurement
Optimal probe states for phase estimation under covariant measurements are given by the principal eigenvector of a Toeplitz matrix constructed from the cost function, achieving Heisenberg scaling for a specific cost.