The estimation of all the parameters in an unknown quantum state or measurement device, commonly known as quantum state tomography (QST) and quantum detector tomography (QDT), is crucial for comprehensively characterizing and controlling quantum systems. In this article, we introduce a framework, in two different bases, that utilizes multiple quantum processes to simultaneously identify a quantum state and a detector. We develop a closed-form algorithm for this purpose and prove that the mean squared error scales as O(1/N) for both QST and QDT, where N denotes the total number of state copies. This scaling aligns with established patterns observed in previous works that addressed QST and QDT as independent tasks. Furthermore, we formulate the problem as a sum of squares optimization problem with semialgebraic constraints, where the physical constraints of the state and detector are characterized by polynomial equalities and inequalities. The effectiveness of our proposed methods is validated through numerical examples.
Publication:
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
http://dx.doi.org/10.1109/TAC.2025.3635368
Author:
Xiao, Shuixin
Univ New South Wales, Sch Engn & Technol, Canberra, ACT 2600, Australia
Australian Natl Univ, Sch Engn, Canberra, ACT 2601, Australia
Univ Melbourne, Dept Elect & Elect Engn, Parkville, Vic 3010, Australia
Email address:shuixin.xiao@anu.edu.au
Liang, Weichao
Univ New South Wales, Sch Engn & Technol, Canberra, ACT 2600, Australia
Xi An Jiao Tong Univ, Fac Elect & Informat Engn, Sch Automat Sci & Engn, Xian 710049, Peoples R China
Email address:weichao.liang@xjtu.edu.cn
Ugrinovskii, Valery
Univ New South Wales, Sch Engn & Technol, Canberra, ACT 2600, Australia
Petersen, Ian R.
Australian Natl Univ, Sch Engn, Canberra, ACT 2601, Australia
Email address:i.r.petersen@gmail.com
Wang, Yuanlong (corresponding author)
Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Email address:wangyuanlong@amss.ac.cn
Dong, Daoyi
Univ Technol Sydney, Australian Artificial Intelligence Inst, Fac Engn & Informat Technol, Sydney, NSW 2007, Australia
Email address:daoyidong@gmail.com
附件下载：
