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Classically high-dimensional correlation: simulation of high-dimensional entanglement.

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    Area of Science:

    • Quantum Information Science
    • Classical and Quantum Correlations

    Background:

    • Classical correlation is vital for quantum and classical systems, enhancing precision and channel characterization.
    • Current classical correlation methods are limited to two orthogonal bases, restricting dimensionality.
    • Extending correlation dimensionality is crucial for advanced quantum information processing.

    Purpose of the Study:

    • To introduce a novel, high-dimensional classical correlation.
    • To demonstrate its mathematical equivalence to quantum correlations.
    • To explore its applications in simulating Bell inequality violations and characterizing quantum channels.

    Main Methods:

    • Developing a theoretical framework for high-dimensional classical correlation.
    • Establishing mathematical equivalence between classical and quantum correlations in higher dimensions.
    • Simulating high-dimensional Bell inequality violations.
    • Theoretically analyzing quantum channel characterization under atmospheric turbulence.

    Main Results:

    • A new form of high-dimensional classical correlation has been established.
    • This classical correlation can simulate violations of high-dimensional Bell inequalities.
    • The proposed scheme offers robust characterization of quantum channels with high-dimensional states, even with atmospheric perturbations.

    Conclusions:

    • The study introduces a powerful tool for high-dimensional classical correlation, bridging classical and quantum realms.
    • This work provides new physical insights into classical correlation and its potential.
    • The findings suggest significant applications in high-dimensional quantum information processing and secure communication.