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In this work, we present a family of direct tomography protocols that can characterize various types of high-dimensional photon states. In specific, we show direct tomography approaches that can measure high-dimensional spatial modes, spatial vector modes and partially-coherent modes. In direct tomography methods, the measurement readouts directly correspond to the complex-valued state vector or other quantities that describe the quantum system to be measured, and therefore can significantly reduce the complexity of tomography procedures for high-dimensional states. Moreover, we show that it is possible to design the tomography protocol such that all the information needed to describe the photon states can be acquired in a single experimental setup without any need of scanning. This is particularly interesting for real-time metrology of both quantum and classical photon states. The unique single-shot, direct characterization capability provide powerful real-time metrology tools that can boost fundamental studies and applications of high-dimensional photon states.
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