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    This study introduces a new quantum state tomography method for reconstructing high-dimensional quantum states using fewer experimental settings. The technique achieves high fidelity, significantly improving efficiency in quantum information processing.

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    Area of Science:

    • Quantum information science
    • Quantum optics
    • Quantum state reconstruction

    Background:

    • Quantum state tomography is crucial for characterizing quantum systems.
    • Reconstructing high-dimensional quantum states (qudits) is challenging due to the exponential increase in measurement settings.
    • Existing methods often require a large number of experimental settings, limiting practical applications.

    Purpose of the Study:

    • To develop a novel quantum state tomography method for arbitrary d-dimensional quantum states.
    • To reduce the number of required experimental settings for efficient state reconstruction.
    • To demonstrate the method's efficacy for high-dimensional photonic states.

    Main Methods:

    • Utilized a family of bases enabling spatially multiplexed projective measurements.
    • Developed a method requiring only d+1 experimental settings for d-dimensional state reconstruction.
    • Implemented the scheme for experimental reconstruction of 6-dimensional photonic states.

    Main Results:

    • Achieved high-fidelity reconstruction (above 0.97) for both pure and mixed d-dimensional states.
    • Successfully reconstructed 6-dimensional quantum states where complete sets of mutually unbiased bases do not exist.
    • Reduced the number of experimental settings from 42 to 7 for d=6 states.

    Conclusions:

    • The proposed quantum state tomography method is highly efficient for reconstructing high-dimensional quantum states.
    • This technique overcomes limitations of previous methods, particularly for dimensions lacking complete mutually unbiased bases.
    • The method offers a significant advancement for practical quantum information processing and quantum state characterization.