Quantum tomography by regularized linear regressions

doi:10.1016/j.automatica.2020.108837

CSpace

	Quantum tomography by regularized linear regressions
	Mu, Biqiang 1; Qi, Hongsheng 1,2; Petersen, Ian R.3; Shi, Guodong 4
	2020-04-01
发表期刊	AUTOMATICA
ISSN	0005-1098
卷号	114 页码:15
摘要	In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields random outcomes, from which a classical linear regression model can be established. First of all, for complete or over-complete measurement bases, we show that the empirical data can be utilized for the construction of a weighted least squares estimate (LSE) for quantum tomography. Taking into consideration the trace-one condition, a constrained weighted LSE can be explicitly computed, being the optimal unbiased estimation among all linear estimators. Next, for general measurement bases, we show that l(2)-regularization with proper regularization gain provides even a lower mean-square error under a cost in bias. The optimal regularization parameter is defined in terms of a risk characterization for any finite sample size and a resulting implementable estimator is proposed. Finally, a concise and unified formula is established for the regularization parameter with complete measurement basis under an equivalent regression model, which proves that the proposed implementable tuning estimator is asymptotically optimal as the number of copies grows to infinity. Additionally, several numerical examples are provided to validate the established results. (C) 2020 Elsevier Ltd. All rights reserved.
关键词	Quantum state tomography Linear regression Regularization
DOI	10.1016/j.automatica.2020.108837
收录类别	SCI
语种	英语
资助项目	National Key R&D Program of China[2018YFA0703800] ; National Natural Science Foundation of China[61873262] ; Australian Research Council[DP180101805] ; Australian Research Council[DP190103615]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000519656500014
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50962
专题	中国科学院数学与系统科学研究院
通讯作者	Qi, Hongsheng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Australian Natl Univ, Res Sch Elect Energy & Mat Engn, Canberra, ACT 0200, Australia 4.Univ Sydney, Australian Ctr Field Robot, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW 2006, Australia
推荐引用方式 GB/T 7714	Mu, Biqiang,Qi, Hongsheng,Petersen, Ian R.,et al. Quantum tomography by regularized linear regressions[J]. AUTOMATICA,2020,114:15.
APA	Mu, Biqiang,Qi, Hongsheng,Petersen, Ian R.,&Shi, Guodong.(2020).Quantum tomography by regularized linear regressions.AUTOMATICA,114,15.
MLA	Mu, Biqiang,et al."Quantum tomography by regularized linear regressions".AUTOMATICA 114(2020):15.