Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise
Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise
复制标题
纯态系综与量子高斯白噪声的局部渐近等价
作者：
C. Butucea;M. Guţă;M. Nussbaum
量子技术越来越依赖于专门的统计推断方法来分析量子测量数据。这激发了“量子统计学”的发展，这是一个在量子物理学和“经典”统计学的重叠中形成的领域。迄今为止，研究较少的主题之一是无限维量子系统的统计推断，它可以被视为非参数统计的量子对应物。本文分析了在纯态下完全相同制备的量子系统系综所构成的量子统计模型的渐近理论。在大合奏的限制，我们建立了本地渐近等价（LAE）的这个独立同分布。模型转换为量子高斯白色噪声模型。我们使用LAE的结果，以建立极小极大率属于厄米-索伯列夫类波函数的纯态的估计。此外，对于相同状态的二次函数估计，我们注意到在速率中的肘效应，而对于纯状态的测试，在非参数Hermite-Sobolev类上获得了尖锐的参数速率。;分类-JEL：62 B15; 62 G 05; 62 G10; 81 P50
Quantum technology is increasingly relying on specialised statistical inference methods for analysing quantum measurement data. This motivates the development of "quantum statistics", a field that is shaping up at the overlap of quantum physics and "classical" statistics. One of the less investigated topics to date is that of statistical inference for infinite dimensional quantum systems, which can be seen as quantum counterpart of non-parametric statistics. In this paper we analyse the asymptotic theory of quantum statistical models consisting of ensembles of quantum systems which are identically prepared in a pure state. In the limit of large ensembles we establish the local asymptotic equivalence (LAE) of this i.i.d. model to a quantum Gaussian white noise model. We use the LAE result in order to establish minimax rates for the estimation of pure states belonging to Hermite-Sobolev classes of wave functions. Moreover, for quadratic functional estimation of the same states we note an elbow effect in the rates, whereas for testing a pure state a sharp parametric rate is attained over the nonparametric Hermite-Sobolev class. ;Classification-JEL: 62B15; 62G05; 62G10; 81P50
低阶态的光谱阈值量子断层扫描
影响因子：
3.3
作者：
Butucea C
通讯作者：
Butucea C