N-body-extended Channel Estimation for Low-Noise Parameters

Details N-body-extended Channel Estimation for Low-Noise Parameters N-body-extended Channel Estimation for Low-Noise Parameters

2006-09-28

arxiv.org/abs/quant-ph/0609218v1

J. Phys. A: Math. Gen. 39 No 46 (17 November 2006) 14465-14470

Physics

Quantum Physics

10 pages, 1 figure

Scientific paper

10.1088/0305-4470/39/46/015

The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005)]. An estimation theory of low-noise parameters of channels has also been developed. In this report, we address the low-noise parameter estimation problem for the $N$-body extension of low-noise channels. We perturbatively calculate the Fisher information of the output states in order to evaluate the lower-bound of the mean-square error of the parameter estimation. We show that the maximum of the Fisher information over all input states can be attained by a factorized input state in the leading order of the low-noise parameter. Thus, to achieve optimal estimation, it is not necessary for there to be entanglement of the $N$ subsystems, as long as the true low-noise parameter is sufficiently small.

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