Quantum tomography by regularized linear regressions
文献类型：期刊论文
| 作者 | Mu, Biqiang3; Qi, Hongsheng1,3; Petersen, Ian R.2; Shi, Guodong4 |
| 刊名 | AUTOMATICA
 |
| 出版日期 | 2020-04-01 |
| 卷号 | 114页码:15 |
| 关键词 | Quantum state tomography Linear regression Regularization |
| ISSN号 | 0005-1098 |
| DOI | 10.1016/j.automatica.2020.108837 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000519656500014 |
| 出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50961]  |
| 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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Australian Natl Univ, Res Sch Elect Energy & Mat Engn, Canberra, ACT 0200, Australia 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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