A tight Cram?r?Rao bound for joint parameter estimation with a pure two-mode squeezed probe

Abstract

We calculate the Holevo Cramér–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 . 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.