The Holevo Cramér-Rao bound is a lower bound on the sum of the mean-square error of estimates for parameters of a state. We provide a method for calculating the Holevo Cramér-Rao bound for estimation of quadrature mean parameters of a Gaussian state by formulating the problem as a semidefinite program. In this case, the bound is tight; it is attained by purely Gaussian measurements. We consider the example of a symmetric two-mode squeezed thermal state undergoing an unknown displacement on one mode. We calculate the Holevo Cramér-Rao bound for joint estimation of the conjugate parameters for this displacement. The optimal measurement is different depending on whether the state is entangled or separable.
The 2023 Boyer Lecture series is called 'The Atomic Revolution' and is presented by Professor Michelle Simmons AO, a pioneer in atomic electronics and global leader in quantum computing.READ
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