Experimental certification of quantum dimensions and irreducible high-dimensional quantum systems with independent devices

Dimensionality plays an important role in various information-theoretic tasks and can be seen as a key resource for quantum information processing. In this work, for the first time to the best of our knowledge, we report an experimental test of classical and quantum dimensions in a prepare-and-measure scenario through a nonlinear dimension witness (NDW), where the preparer and the measurer have no shared randomness. We propose a theoretical method to certify whether the generated states can be decomposed as products of lower dimensional states with the NDW, certify the dimension of the high-dimensional system, and identify whether the quantum system is irreducible in a unified picture in our experiment. To demonstrate the practicability of this method, we experimentally witness the generation of classical and quantum systems encoded in the high-dimensional orbital angular momentum (OAM) state under the effects of atmospheric turbulence. Our results show that this nonlinear dimension witness is highly robust and can be used in the presence of noise and low detection efficiency; hence, we estimate the dimension in our experiment in a detection loophole-free manner through the NDW. We believe our work opens new avenues for dimension witnesses, especially for device-independent estimation of quantum systems and quantum communications. (c) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement