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Upper bounds on the Holevo Cram\'er-Rao bound for multiparameter quantum parametric and semiparametric estimation
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We formulate multiparameter quantum estimation in the parametric and semiparametric setting. While the Holevo Cram\'er-Rao bound (CRB) requires no substantial modifications in moving from the former to the latter, we generalize the Helstrom CRB appropriately. We show that the Holevo CRB cannot be greater than twice the generalized Helstrom CRB. We also present a tighter, intermediate, bound. Finally, we show that for parameters encoded in the first moments of a Gaussian state there always exists a Gaussian measurement that gives a classical Fisher information matrix that is one-half of the quantum Fisher information matrix.
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Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach
High-precision shadow tomography of unknown quantum states has sample complexity Θ~(Γ_p/ε²), with Γ_p characterized by the inverse Fisher information matrix of the optimal single-copy measurement.
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