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Cyclic transformation of orbital angular momentum modes

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Article number043019
Number of pages8
JournalNew Journal of Physics
Publication statusPublished - 14 Apr 2016
Externally publishedYes
Publication typeA1 Journal article-refereed


The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D-dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D-dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.


  • photonic orbital angular momentum, quantum transformation, computer-designed experiment, high-dimensional Hilbert-space, cyclic transformation, ENTANGLEMENT, LIGHT