Simultaneous estimations of quantum state and detector through multiple quantum processes

• URL: http://arxiv.org/abs/2502.11772v1
• Date: Mon, 17 Feb 2025 13:02:36 GMT
• Title: Simultaneous estimations of quantum state and detector through multiple quantum processes
• Authors: Shuixin Xiao, Weichao Liang, Yuanlong Wang, Daoyi Dong, Ian R. Petersen, Valery Ugrinovskii,
• Abstract summary: We introduce a framework, in two different bases, that utilizes multiple quantum processes to simultaneously identify a quantum state and a detector. We prove that the mean squared error (MSE) scales as $O(1/N) $ for both QST and QDT, where $N $ denotes the total number of state copies.
• Score: 4.782967012381978
• License:
• Abstract: 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 paper, 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 (MSE) 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 (SOS) 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.

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