Attaining the Ultimate Precision Limit in Quantum State Estimation
Attaining the Ultimate Precision Limit in Quantum State Estimation
复制标题
达到量子态估计的终极精度极限
DOI：
10.1007/s00220-019-03433-4
复制
发表时间：
2019-05-01
影响因子：
2.4
通讯作者：
Hayashi, Masahito
中科院分区：
文献类型：
--
作者：
Yang, Yuxiang;Chiribella, Giulio;Hayashi, Masahito
本文给出了有限维量子系统状态估计精度的一个界，并证明了它在谱非简并的一般情况下的可达性。我们的结果下，称为局部渐近协方差，这是弱于无偏性或局部无偏性的假设。推导是基于对估计的偏离参数的真实值的极限分布的分析，并利用量子局部渐近正态性，一个有用的渐近表征相同的准备状态的高斯状态。我们首先证明了我们的结果的均方误差的一类特殊的模型，所谓的D-不变，然后将结果扩展到任意模型，通用成本函数，和全局状态估计，其中未知参数不限于本地邻域的真值。该扩展包括对干扰参数的处理，即实验者不感兴趣但仍然影响估计精度的参数。作为一般方法的一个例子，我们提供了最佳的估计策略的联合测量的两个量子比特可观的，在振幅阻尼噪声的存在下的量子比特状态的估计，和嘈杂的多相估计。
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator’s deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, calledD-invariant, and then extend the results to arbitrary models, generic cost functions, and global state estimation, where the unknown parameter is not restricted to a local neighbourhood of the true value. The extension includes a treatment of nuisance parameters, i.e. parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation. As an illustration of the general approach, we provide the optimal estimation strategies for the joint measurement of two qubit observables, for the estimation of qubit states in the presence of amplitude damping noise, and for noisy multiphase estimation.