title: Quantum state tomography via linear regression estimation.
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.
authors: Key Laboratory of Systems and Control, ISS, and National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, CAS, Beijing 100190, P. R. China.
authors: Bo
authors: B
authors: Qi
authors: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China.
authors: Zhibo
authors: Z
authors: Hou
authors: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China.
authors: Li
authors: L
authors: Li
authors: School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia.
authors: Daoyi
authors: D
authors: Dong
authors: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China.
authors: Guoyong
authors: G
authors: Xiang
authors: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, P. R. China.
authors: Guangcan
authors: G
authors: Guo