Simultaneous Estimations of Quantum State and Detector Through Multiple Quantum Processes

• 成果类型: Article
• 署名作者: Xiao, Shuixin; Liang, Weichao; Wang, Yuanlong; Dong, Daoyi; Petersen, Ian R.; Ugrinovskii, Valery
• 署名单位: University of New South Wales Sydney; Australian National University; University of Melbourne; Xi'an Jiaotong University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; University of Technology Sydney; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3635368
• 发表日期: 2026
• 关键词: SYSTEM-IDENTIFICATION; tomography

摘要

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.