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Quantum local asymptotic normality based on a new quantum likelihood ratio. (English) Zbl 1278.81050

Summary: We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.

MSC:

81P50 Quantum state estimation, approximate cloning
62F12 Asymptotic properties of parametric estimators
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References:

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