Distinguishing between strings of data or waveforms is at the core of multiple applications in information technologies. In a quantum language the task is to design protocols to differentiate quantum states. Quantum-based technologies promises to go beyond the capabilities offered by technologies based on classical principles. However the implementation of the logical gates that are the core of these systems is challenging since they should overcome quantum decoherence, low probability of success and are prone to errors. One unexpected contribution of considering ideas in the quantum world is to inspire similar solutions in the classical world (quantum-inspired technologies), protocols that aim at mimicking particular features of quantum algorithms. This is based on features of quantum physics also shared by waves in the classical world, such it is the case of interference or entanglement between degrees of freedom of a single particle. Here we demonstrate in a proof-of-concept experiment a new type of quantum-inspired protocol based on the idea of quantum fingerprinting (Phys. Rev. Lett. 87, 167902, 2001). Information is encoded on optical beams with orbital angular momentum (OAM). These beams allow to implement a crucial element of our system, a new type of Fredkin gate or polarization-controlled SWAP operation that exchange data between OAM beams. The protocols can evaluate the similarity between pairs of waveforms and strings of bits and quarts without unveiling the information content of the data.
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