Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are informationally complete or informationally incomplete. In the informationally complete scenario, without regularization, we optimize the resource (probe state) distribution by converting it to a semidefinite programming problem. Then in both the informationally complete and informationally incomplete scenarios, we discuss different regularization forms and prove the mean squared error scales as O(1/N) or tends to a constant with N state copies under the static assumption. We also characterize the ideal best regularization for the identifiable parameters, accounting for both the informationally complete and informationally incomplete scenarios. Numerical examples demonstrate the effectiveness of different regularization forms and a quantum optical experiment test shows that a suitable regularization form can reach a reduced mean squared error.  

　　Publication:  

　　Automatica, Volume 155, September 2023, 111124  

　　http://dx.doi.org/10.1016/j.automatica.2023.111124  

　　Author:  

　　Shuixin Xiao  

　　University of Michigan – Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China  

　　School of Engineering and Information Technology, University of New South Wales, Canberra ACT 2600, Australia  

　　Yuanlong Wang  

　　Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China  

　　Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia  

　　Email: wangyuanlong@amss.ac.cn  

　　Jun Zhang  

　　University of Michigan – Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China  

　　Daoyi Dong  

　　School of Engineering and Information Technology, University of New South Wales, Canberra ACT 2600, Australia  

　　Shota Yokoyama  

　　School of Engineering and Information Technology, University of New South Wales, Canberra ACT 2600, Australia  

　　Centre for Quantum Computation and Communication Technology, Australian Research Council, Canberra, ACT 2600, Australia  

　　Ian R. Petersen  

　　School of Engineering, Australian National University, Canberra, ACT 2601, Australia  

　　Hidehiro Yonezawa  

　　School of Engineering and Information Technology, University of New South Wales, Canberra ACT 2600, Australia  

　　Centre for Quantum Computation and Communication Technology, Australian Research Council, Canberra, ACT 2600, Australia