A simple argument is presented that explicitly shows how to construct an arbitrary quantum gate acting on orbital angular momentum (OAM) of single photons. The scheme can be applied to implement subspace multiplexing, where a single high-dimensional OAM qudit represents effectively a stack of multiple independent lower-dimensional qudits. A special subclass of unitaries composed of single-photon controlled gates is studied in detail and notable examples of the general approach are discussed. The generalization of the simple argument leads to the parallelization scheme, which results in the savings of resources. The presented schemes utilize only conventional optical elements and apply not only to single photons but also to classical light.

中文翻译：

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单光子轨道角动量中的任意酉

提出了一个简单的论点，明确地展示了如何构造一个作用于单光子轨道角动量 (OAM) 的任意量子门。该方案可用于实现子空间复用，其中单个高维 OAM qudit 有效地表示多个独立的低维 qudit 的堆栈。详细研究了由单光子控制门组成的一个特殊子类，并讨论了一般方法的显着示例。简单参数的泛化导致并行化方案，从而节省资源。所提出的方案仅利用传统的光学元件，不仅适用于单光子，也适用于经典光。