  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.
