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Orbital angular momentum (OAM) of light is a promising degree of freedom forquantum communication and quantum computation. However, efficient methods totransform and measure OAM modes are still not available readily. Here, wepropose a method for full quantum state tomography for arbitrary OAM states oflight. The key component in our scheme is the helicity sorter, a device thatcan sort OAM modes of a light beam based on their Helicity. We present twosetups to implement the Helicity sorted, one requires $\mathcal{O}(N)$ numberof optical elements for $2^N$ OAM modes, and the other uses spatial lightmodulators and is independent of the number of OAM modes. Ours is the firstmethod to provide the efficient and scalable full quantum state tomography ofthe OAM modes and can be extremely important for quantum communication andquantum computation.

Efficient full state tomography of the orbital angular momentum states of light using Helicity sorter