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Rank-based model selection for multiple ions quantum tomography

Guţă, Mădălin; Kypraios, Theodore; Dryden, Ian

Authors

Mădălin Guţă

Theodore Kypraios

Ian Dryden



Abstract

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)—two models consisting 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 four 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 four ions experiment aimed at creating a Smolin state of rank 4. By applying the two methods together with the Pearson χ2 test we conclude that the data can be suitably described with a model whose rank is between 7 and 9. 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.

Journal Article Type Article
Publication Date Oct 1, 2012
Journal New Journal of Physics
Electronic ISSN 1367-2630
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 14
Issue 105002
Institution Citation Guţă, M., Kypraios, T., & Dryden, I. (2012). Rank-based model selection for multiple ions quantum tomography. New Journal of Physics, 14(105002), doi:10.1088/1367-2630/14/10/105002
DOI https://doi.org/10.1088/1367-2630/14/10/105002
Publisher URL http://iopscience.iop.org/1367-2630/14/10/105002/
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nd-sa/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nd-sa/4.0





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