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We investigate the intrinsic uncertainty in the accuracy to which a staticspacetime can be measured from scattering experiments. In particular, we focuson the Schwarzschild black hole and a spatially kinked metric that has somemathematical resemblance to an expanding universe. Under selected conditions wefind that the scattering problem can be framed in terms of a lossy bosonicchannel, which allows us to identify shot-noise scaling as the ultimatescaling-limit to the estimation of the spacetimes. Fock state probes withparticle counting measurements attain this ultimate scaling limit and thescaling constants for each spacetime are computed and compared to the practicalstrategies of coherent state probes with heterodyne and homodyne measurements.A promising avenue to analyze the quantum-limit of the analogue spacetimes inoptical waveguides is suggested.

Gravitational parameter estimation in a waveguide