We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.
@article{arxiv.1207.5904,
title = {Possibility of Upper-Bounding Dimension of Quantum States Device-Independently},
author = {Won-Young Hwang},
journal= {arXiv preprint arXiv:1207.5904},
year = {2014}
}