Simultaneous quantum state and detector tomography through multiple Hamiltonians

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Shuixin Xiao, Weichao Liang, Yuanlong Wang, Daoyi Dong, Ian R. Petersen, Valery A. Ugrinovskii

Published: 2024, Last Modified: 21 Jan 2026CDC 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: The estimation of all the parameters in an unknown quantum state/measurement device, commonly referred to as quantum state/detector tomography (QST/QDT), plays a pivotal role in characterization and control of quantum systems. In this paper, we introduce a novel method to concurrently identify a quantum state and a detector using multiple Hamiltonians. We then develop two solutions, i.e., a closed-form algorithm and the sum of squares (SOS) optimization. The numerical examples demonstrate that the closed-form solution offers computational efficiency, while the SOS optimization method ensures accuracy.