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arXiv · 1003.4575

Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation

Masahito Hayashi
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Abstract

In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the minimum mean square error decreases with the order O(1/n).

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Masahito Hayashi. 2010-10-28. Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation. https://doi.org/10.1007/s00220-011-1239-4

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