Fourier State Tomography of Polarization-Encoded Qubits

Abstract: Quantum state tomography is a central technique for the characterization and verification of quantum systems. Standard tomography is widely used for low-dimensional systems, but for larger systems, it becomes impractical due to the exponential scaling of experimental complexity with the number of qubits. Here, we present an experimental realization of Fourier-transform quantum state tomography for polarization-encoded photonic states. We validate the technique using weak coherent states and entangled photon pairs generated by a quantum dot and spontaneous parametric down-conversion source in the telecom wavelength. The reconstructed density matrices show excellent agreement with those obtained through conventional projective tomography, with calculated metrics such as fidelity and concurrence matching within error bars, confirming the reliability and accuracy of the technique. Fourier state tomography employs only a single rotating waveplate per qubit, thereby avoiding repeated adjustments across multiple waveplates and ensuring that the number of physical measurement settings scales linearly with the number of qubits, despite the exponential growth of the underlying state space. This reduction in optical configurations simplifies experimental overhead, making Fourier state tomography a practical alternative for multi-qubit characterization.