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    Area of Science:

    • Quantum optics
    • Classical optics
    • Entanglement theory

    Background:

    • Partially coherent vector light fields exhibit complex polarization-spatial correlations.
    • Detecting bipartite entanglement in such fields is crucial for quantum information science.
    • Existing methods may not fully capture entanglement in these systems.

    Purpose of the Study:

    • To introduce a generalized uncertainty principle for polarization-spatial degrees of freedom.
    • To develop a method for detecting bipartite entanglement in partially coherent paraxial vector light fields.
    • To demonstrate the necessity and sufficiency of partial transpose for a specific class of these fields.

    Main Methods:

    • Introduction of a generalized uncertainty principle tailored for polarization-spatial correlations.
    • Application of partial transpose implemented via the generalized uncertainty principle.
    • Analysis of partially coherent vector light fields with Gaussian spatial profiles.

    Main Results:

    • A novel generalized uncertainty principle is established.
    • Partial transpose is shown to be a necessary and sufficient criterion for entanglement detection in the studied fields.
    • The method is effective for partially coherent vector light fields with Gaussian spatial characteristics.

    Conclusions:

    • The developed generalized uncertainty principle provides a robust tool for entanglement detection.
    • The findings facilitate the study and application of entangled light fields.
    • An experimental scheme using classical optical interferometry is proposed for realizing these entangled states.