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

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

2010-03-24

arxiv.org/abs/1003.4575v3

Communications in Mathematical Physics, Vol. 304, No. 3, 689-709 (2011)

Physics

Quantum Physics

In this revision, some unlcear parts are clarified

Scientific paper

10.1007/s00220-011-1239-4

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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