N-body-extended channel estimation for low-noise parameters

The notion of low-noise channels was recently proposed and analysed in detail in order to describe noise-processes driven by the environment (Hotta M, Karasawa T and Ozawa M 2005 Phys. Rev. A 72 052334). An estimation theory of low-noise parameters of channels has also been developed. In this paper, we address the low-noise parameter estimation problem for the N-body extension of the dissipative 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 and the channel is properly dissipative.