Asymptotic inference in system identification for the atom maser.
Asymptotic inference in system identification for the atom maser.
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原子脉泽系统辨识中的渐近推理。
DOI：
10.1098/rsta.2011.0528
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Catana C
中科院分区：
文献类型：
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作者：
Catana C
系统辨识与控制理论密切相关，在量子工程中发挥着越来越重要的作用。在量子设置中，系统识别通常等同于过程断层扫描，即通过使用不同的输入状态重复探测通道来估计通道。然而，对于诸如量子马尔可夫过程之类的量子动力系统，更自然的是考虑基于输出的连续测量的估计，并且给定的输入可能是固定的。我们使用渐近统计工具来解决这个问题，例如估计原子脉泽的拉比频率的具体示例。我们计算了不同测量过程的费希尔信息以及原子微波激射器的量子费希尔信息，并建立了这些统计模型的局部渐近正态性。统计概念可以用某些变形马尔可夫生成器的谱特性来表达，并且简要讨论了与大偏差的联系。
System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.