We calculate the Holevo Cram\'er-Rao bound for estimation of the displacement experienced by one mode of an two-mode squeezed vacuum state with squeezing r and find that it is equal to 4exp(-2r). This equals the sum of the mean squared error obtained from a dual homodyne measurement, indicating that the bound is tight and that the dual homodyne measurement is optimal.
Cite
@article{arxiv.1702.02271,
title = {A tight Cram\'er-Rao bound for joint parameter estimation with a pure two-mode squeezed probe},
author = {Mark Bradshaw and Syed M Assad and Ping Koy Lam},
journal= {arXiv preprint arXiv:1702.02271},
year = {2019}
}