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arXiv 1206.4032quant-phstat.AP
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基于秩的多离子量子成像模型选择

Rank-based model selection for multiple ions quantum tomography

Madalin Guta, Theodore Kypraios, Ian Dryden

备注：
24 pages, 6 figures, 3 tables
发表信息：
New J. Phys. (14) 105002, 2012
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摘要：

测量数据的统计分析已成为许多量子工程实验的关键组成部分。由于标准的全态层析成像对于大维度量子系统变得不可行，因此需要利用实验状态的先验信息和“稀疏性”性质来降低估计问题的维数。在本文中，我们提出了模型选择的一般原则，找到最简单的，或最简约的解释的数据，通过拟合不同的模型，并选择估计与最佳的权衡之间的似然拟合和模型的复杂性。我们将两种成熟的模型选择方法--赤池信息准则（AIC）和贝叶斯信息准则（BIC）--应用于由固定秩状态和当前在多离子实验中产生的数据集组成的模型。我们测试了AIC和BIC对随机选取的4个离子的低阶态的性能，并研究了所选的阶数与测量重复次数的关系。然后，我们将该方法应用于实际数据的4离子实验，旨在创建一个斯莫林状态的秩4。这两种方法表明，描述数据的最佳模型位于秩6和9之间，并应用Pearson $χ^{2}$检验来验证这一结论。此外，我们发现，纯状态的极大似然估计的均方误差是接近的最佳的所有可能的测量。

英文摘要：

The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the "sparsity" properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods -- the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) -- to models consising of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of 4 ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a 4 ions experiment aimed at creating a Smolin state of rank 4. The two methods indicate that the optimal model for describing the data lies between ranks 6 and 9, and the Pearson $χ^{2}$ test is applied to validate this conclusion. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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