Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this problem in the prepare-and-measure scenario. Specifically, we provide a lower bound on the dimension of the prepared quantum systems which is a function that only depends on the measurement statistics. Furthermore, we show that our bound performs well on several examples. {In particular}, we show that our bound provides new insights into the notion of dimension witness, and we also use it to show that the sets of restricted-dimensional prepare-and-measure correlations are not always convex.
@article{arxiv.1606.03878,
title = {Device-independent dimension tests in the prepare-and-measure scenario},
author = {Jamie Sikora and Antonios Varvitsiotis and Zhaohui Wei},
journal= {arXiv preprint arXiv:1606.03878},
year = {2016}
}