低噪声参数下的N体扩展信道估计
N-body-extended Channel Estimation for Low-Noise Parameters
摘要：
低噪声信道的概念是近年来提出的，并对其进行了详细的分析，以描述环境驱动的噪声过程[M。霍塔，T. Karasawa和M. Ozawa，Phys.Rev.A72，052334（2005）]。本文还提出了信道低噪声参数的估计理论。在这份报告中，我们解决了低噪声参数估计问题的$N$体扩展的低噪声通道。我们微扰计算输出状态的Fisher信息，以评估参数估计的均方误差的下限。我们表明，在所有的输入状态的Fisher信息的最大值可以通过一个因式分解的输入状态的低噪声参数的领先顺序。因此，为了实现最佳估计，不需要存在$N$子系统的纠缠，只要真正的低噪声参数足够小。
英文摘要：
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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