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IEEE International Conference on Quantum Control, Computing and Learning (qCCL)

Collective Quantum State Tomography: Closed-Form and Numerical Solutions, and Validation

Shuixin Xiao, Yuanlong Wang, Zhibo Hou, Guo‐Yong Xiang, Ian R. Petersen, Daoyi Dong

Published Jun 25, 2025• 0 citations
Publisher

Abstract

Quantum state tomography (QST) is a technique for characterizing, benchmarking, and verifying quantum systems and devices. In this paper, we focus on collective QST using data from collective measurements performed on multiple copies of the state. We propose a closed-form solution and provide an analytical characterization of its computational complexity and mean squared error (MSE) scaling. Additionally, we reformulate the problem as a sum of squares (SOS) optimization problem with semialgebraic constraints, enabling the application of SOS tools for its solution. The effectiveness of the proposed methods is demonstrated through numerical simulations. Furthermore, we validate the algorithms using two-copy collective experimental data, where the entangled measurement provides information about the state purity. Compared to previous methods, our algorithms achieve lower MSEs and approach the collective MSE bound by leveraging this purity information more efficiently.

DOI
10.1109/qccl65142.2025.11158864

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Quantum state tomography (QST) is a fundamental technique for characterizing quantum states, crucial for validating quantum technologies. However, traditional QST methods often suffer from limitations in measurement efficiency and accuracy, particularly when dealing with complex quantum systems. This work presents an advanced approach to QST utilizing entangled photon sources and a meticulously designed measurement strategy. The core of this method lies in exploiting the correlations inherent in entangled photon pairs to significantly enhance the reconstruction process. We detail a novel scheme that minimizes measurement errors and maximizes the information extracted from each measurement, leading to a substantial improvement in both the accuracy and resolution of the reconstructed quantum state. The theoretical framework outlines the key equations and algorithms used for state reconstruction, focusing on a practical implementation. The results presented suggest a pathway towards more robust and reliable QST, paving the way for more accurate characterization of quantum systems and the development of advanced quantum applications.
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