Kramers–Kronig relations and precision limits in quantum phase estimation

Phase measurements are of paramount importance in quantum optical sensing. However, the promise a advantage, celebrated Heisenberg scaling, is severely curtailed presence noise and loss. Here we investigate systems which phase absorption profiles linked by Kramers–Kronig relations show that, limit large photon number, their use connects uncertainties on attainable optimal probes for loss phase. This underlines physical motivation scaling lost. Our results bear practical implications, revealing metrological capabilities determining profiles.