Parallelized projective measurements for spatial photonic qudits estimation

We present a quantum state tomography method that enables the reconstruction of arbitrary d−dimensional quantum states encoded in the discretized transverse momentum of photons, by using only d + 1 experimental settings. To this end, we identify a family of bases with the property that the outcomes of a projective measurement are spatially multiplexed on the interference pattern of the projected state. Using the proposed scheme we performed, as a proof-of-principle, an experimentalreconstruction of d = 6−dimensional states, for which a complete set of mutually unbiased bases does not exist. We obtained fidelity values above 0.97 for both pure and mixed states, reducing the number of experimental settings from 42 to only 7. Fil: Pears Stefano, Quimey Martín. Universidad del País Vasco; España. Consejo Superior de Investigaciones Científicas; España Fil: Rebón, Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina