Quantum estimation for non-differentiable models
Quantum estimation for non-differentiable models
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DOI：
10.1088/0305-4470/38/7/014
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发表时间：
2002-07
期刊：
影响因子：
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通讯作者：
Y. Tsuda;Keiji Matsumoto
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文献类型：
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作者：
Y. Tsuda;Keiji Matsumoto
状态估计是量子信息学中的经典问题。在估计方案的优化中，寻找估计器误差的下界是非常重要的一步。到目前为止，所有提出的易于处理的下界都使用密度矩阵的导数。然而，有时我们感兴趣的是具有奇异性的量，例如共生等。在本文中，对于没有光滑性假设的量子估计问题，我们得到了估计器的均方误差的下界。我们的主要思想是用差来代替导数，就像在经典估计理论中所做的那样。我们将这些不等式应用于几个例子，并给出了其中一些例子的最优估计。
State estimation is a classical problem in quantum information. In optimization of an estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use a derivative of the density matrix. However, sometimes, we are interested in quantities with singularity, e.g. concurrence etc. In this paper, lower bounds to a mean square error of an estimator are derived for a quantum estimation problem without smoothness assumptions. Our main idea is to replace the derivative by difference, as is done in classical estimation theory. We applied the inequalities to several examples, and derived an optimal estimator for some of them.