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Quantum theory allows information to flow through a single device in a coherent superposition of two opposite directions, resulting into situations where the input-output direction is indefinite. Here we introduce a theoretical method to witness input-output indefiniteness in a single quantum device, and we experimentally demonstrate it by constructing a photonic setup that exhibits input-output indefiniteness with a statistical significance exceeding 69 standard deviations. Our results provide a way to characterize input-output indefiniteness as a resource for quantum information and photonic quantum technologies and enable table-top simulations of hypothetical scenarios exhibiting quantum indefiniteness in the direction of time.