QUANTUM ESTIMATION FOR QUANTUM TECHNOLOGY
QUANTUM ESTIMATION FOR QUANTUM TECHNOLOGY
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DOI：
10.1142/s0219749909004839
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发表时间：
2009-01-01
影响因子：
1.2
通讯作者：
Paris, Matteo G. A.
中科院分区：
文献类型：
--
作者：
Paris, Matteo G. A.
量子信息中的几个感兴趣的量，包括纠缠和纯度，是密度矩阵的非线性函数，即使在原则上，也不能对应于适当的量子观测值。任何旨在确定这些量的值的方法都应该采用间接测量，因此对应于参数估计问题，其解决方案，即确定最精确的估计量，必然涉及优化过程。我们回顾了局域量子估计理论，给出了相关量子态族的对称对数导数和量子Fisher信息的显式公式。参数的可估计性是根据量子信噪比和实现给定相对误差所需的测量次数来定义的。讨论了优化过程与量子统计模型几何结构之间的联系。我们的分析可以量化量子噪声在测量不可观测的数量，并提供了一个工具，在量子技术中的信号和设备的表征。
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e. the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The connections between the optmization procedure and the geometry of quantum statistical models are discussed. Our analysis allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices in quantum technology.