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arXiv:1304.6827 · Scientific Reports

Quantum State Tomography via Linear Regression Estimation

Bo Qi, Zhibo Hou, Li Li, Daoyi Dong, Guo‐Yong Xiang, Guang‐Can Guo

Published Dec 13, 2013• 156 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep03496

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