Inspired by the classical phenomenon of random walk, the concept of quantum walk has emerged recently as a powerful platform for the dynamical simulation of complex quantum systems, entanglement production and universal quantum computation. Such a wide perspective motivates a renewing search for efficient, scalable and stable implementations of this quantum process. Photonic approaches have hitherto mainly focused on multi-path schemes, requiring interferometric stability and a number of optical elements that scales quadratically with the number of steps. Here we report the experimental realization of a quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous indistinguishable photons. The whole process develops in a single light beam, with no need of interferometers, and requires optical resources scaling linearly with the number of steps. Our demonstration introduces a novel versatile photonic platform for implementing quantum simulations, based on exploiting the transverse modes of a single light beam as quantum degrees of freedom.
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