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Dynamic Programming for Quantum State Tomography with Entangled Photon Sources

Jincheng Zhang

Published Sep 5, 2026• 0 citations
Publisher

Abstract

Quantum state tomography (QST) is a fundamental procedure in quantum information science, enabling the precise characterization of quantum states. Traditional QST methods often require a prohibitive number of measurements, particularly for complex quantum states, significantly limiting their practical application. This work presents a novel approach to QST leveraging dynamic programming. The core idea is to iteratively refine a quantum state estimate based on measurement data, minimizing the total number of measurements needed to achieve a desired level of accuracy. The algorithm constructs a dynamic programming table, storing partial state estimates and their associated probabilities, allowing for efficient exploration of the state space. We demonstrate the efficacy of this approach through theoretical analysis and illustrate its potential advantages over conventional methods. The key contribution lies in the algorithm's ability to adaptively adjust the measurement strategy, focusing on regions of the state space with the highest uncertainty, leading to a substantial reduction in measurement requirements. The performance of the algorithm is discussed in terms of computational complexity and accuracy achieved.

DOI
10.5281/zenodo.22335217

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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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Quantum state tomography (QST) is a crucial technique for characterizing quantum states, vital for verifying quantum device performance and implementing quantum information processing. However, traditional QST methods are notoriously computationally demanding, requiring extensive experimental data acquisition and subsequent processing, often leading to high resource consumption. This work presents a novel framework for QST utilizing probabilistic programming. The core idea is to model the quantum state as a probability distribution and employ Bayesian inference, coupled with variational methods, to efficiently infer the density matrix from limited measurement data. We demonstrate the efficacy of this approach, showcasing its potential to significantly reduce experimental costs and improve the accuracy of QST. The framework's automation and optimization capabilities represent a substantial advancement in the field, paving the way for more accessible and efficient quantum state characterization.
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