Arbitrary d -dimensional Pauli X gates of a flying qudit

-dimensional Pauli 
 gates of a flying qudit},
  author={Xiaoqin Gao and Mario Krenn and Jaroslav Kysela and Anton Zeilinger},
  journal={Physical Review A},
High-dimensional degrees of freedom of photons can encode more quantum information than their two-dimensional counterparts. While the increased information capacity has advantages in quantum applications (such as quantum communication), controlling and manipulating these systems has been challenging. Here we show a method to perform deterministic arbitrary high-dimensional Pauli $X$ gates for single photons carrying orbital angular momentum. The $X$ gate consists of a cyclic permutation of… 

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