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    Area of Science:

    • Quantum information science
    • Quantum optics
    • Photonic quantum technologies

    Background:

    • Quantum state reconstruction is crucial for quantum information processing.
    • Existing quantum tomography methods can be complex and require tunable optical components.

    Purpose of the Study:

    • To develop a novel quantum tomography approach for reconstructing two-photon entangled states.
    • To demonstrate the feasibility of this method in photonic circuits.

    Main Methods:

    • Expanding quantum states across extra degrees of freedom to introduce sparsity.
    • Utilizing measured spatial photon correlations from a discrete-continuous quantum walk.
    • Applying the method to reconstruct any two-photon spatially entangled and mixed state.

    Main Results:

    • Full reconstruction of two-photon spatially entangled and mixed states is achieved.
    • The method leverages inherent sparsity introduced by state expansion.
    • Demonstrated applicability in photonic circuits.

    Conclusions:

    • The proposed quantum tomography approach is efficient and does not require tunable elements.
    • It is well-suited for integration with on-chip superconducting photon detectors.
    • Enables robust characterization of complex photonic quantum states.