Hiding ignorance using high dimensions

Sally Shrapnel, Jacqueline Mary Romero, Michael Kewming, Andrew White

Abstract: 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 [T. Vidick and S. Wehner, Phys. Rev. Lett. 107, 030402 (2011).]. Experimentally verifying this counterintuitive fact requires controlling and measuring quantum systems of high dimension ðd > 9Þ. We provide this experimental evidence using the transverse spatial modes of light, a powerful resource for testing high- dimensional quantum phenomena.