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Quantum networks are the ultimate target in quantum communication, where many connected users can share information carried by quantum systems. The keystones of such structures are the reliable generation, transmission, and manipulation of quantum states. Two-dimensional quantum states, qubits, are steadily adopted as information units. However, high-dimensional quantum states, qudits, constitute a richer resource for future quantum networks, exceeding the limitations imposed by the ubiquitous qubits. The generation and manipulation of such -level systems have been improved over the last ten years, but their reliable transmission between remote locations remains the main challenge. Here, we show how a recent air-core fiber supporting orbital angular momentum (OAM) modes can be exploited to faithfully transmit -dimensional states. Four OAM quantum states and their superpositions are created …