A deterministic construction using the computational basis, the Fourier basis, and d-1 phase-shifted Fourier bases is shown to determine any d-dimensional density matrix, with a d=6 photonic demonstration.
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$d+1$ Measurement Bases are Sufficient for Determining $d$-Dimensional Quantum States: Theory and Experiment
A deterministic construction using the computational basis, the Fourier basis, and d-1 phase-shifted Fourier bases is shown to determine any d-dimensional density matrix, with a d=6 photonic demonstration.