Experimental estimation of the dimension of classical and quantum systems

Abstract

Is it possible to deduce the number of dimensions of a completely unknown system only from the results of measurements performed on it? So-called dimension witnesses allow such an estimation, and are now experimentally demonstrated using pairs of entangled photons. 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 witness1,2,3,4,5,6 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 scenario6. We use photon pairs entangled in polarization and orbital angular momentum 7,8,9 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 new avenues in quantum information science, where dimension represents a powerful resource10,11,12, especially for device-independent estimation of quantum systems13,14,15,16 and quantum communications17,18.