The absence of information -- entirely or partly -- is called ignorance. Naturally, one might ask if some ignorance of a whole system will imply some ignorance of its parts. Our classical intuition tells us yes, however quantum theory tells us no: it is possible to encode information in a quantum system so that despite some ignorance of the whole, it is impossible to identify the unknown part arXiv:1011.6448. Experimentally verifying this counter-intuitive fact requires controlling and measuring quantum systems of high dimension (d>9). We provide this experimental evidence using the transverse spatial modes of light, a powerful resource for testing high dimensional quantum phenomenon.
@article{arxiv.1903.09487,
title = {Hiding Ignorance Using High Dimensions},
author = {M. J. Kewming and S. Shrapnel and A. G. White and J. Romero},
journal= {arXiv preprint arXiv:1903.09487},
year = {2020}
}