Journal
SCIENTIFIC REPORTS
Volume 3, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/srep03496
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Funding
- National Fundamental Research Program [2011CBA00200, 2011CB9211200]
- National Natural Science Foundation of China [61108009, 61222504, 1004049, 61227902, 61374092, 61134008]
- Anhui Provincial Natural Science Foundation [1208085QA08]
- Australian Research Council [DP130101658]
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A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d(4)) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography.
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