The Holevo Cram\'er Rao bound is a lower bound on the sum of the mean squareerror of estimates for parameters of a state. We provide a method forcalculating the Holevo Cram\'er-Rao bound for estimation of quadrature meanparameters of a Gaussian state by formulating the problem as a semidefiniteprogram. In this case, the bound is tight; it is attained by purely Guassianmeasurements. We consider the example of a symmetric two-mode squeezed thermalstate undergoing an unknown displacement on one mode. We calculate the HolevoCram\'er-Rao bound for joint estimation of the conjugate parameters for thisdisplacement. The optimal measurement is different depending on whether thestate is entangled or separable.
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