We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using non-coupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.
@article{arxiv.1710.04601,
title = {Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses},
author = {Edgar A. Aguilar and Máté Farkas and Daniel Martínez and Matías Alvarado and Jaime Cariñe and Guilherme B. Xavier and Johanna F. Barra and Gustavo Cañas and Marcin Pawłowski and Gustavo Lima},
journal= {arXiv preprint arXiv:1710.04601},
year = {2018}
}
Comments
Journal version (except for small editorial modifications), 4+12 pages, 7 figures