Experimental estimation of the dimension of classical and quantum systems

Experimental observations are usually described using theoretical models that make assumptions about the dimensionality of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness(1-6) answers this question, as it allows bounding the dimension of an unknown system only from measurement statistics. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario(6). We use photon pairs entangled in polarization and orbital angular momentum(7-9) to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our work opens newavenues in quantum information science, where dimension represents a powerful resource(10-12), especially for device-independent estimation of quantum systems(13-16) and quantum communications(17,18).