# Hiding Ignorance Using High Dimensions

## TL;DR

This paper demonstrates experimentally that in high-dimensional quantum systems, ignorance of the whole does not necessarily imply ignorance of parts, challenging classical intuition and showcasing unique quantum information properties.

## Contribution

It provides experimental verification of the counter-intuitive quantum property that ignorance of a system does not imply ignorance of its parts in high dimensions.

## Key findings

- Confirmed quantum encoding allows ignorance of the whole without revealing parts
- Controlled high-dimensional quantum systems of dimension > 9 were used
- Experimental results support theoretical predictions about quantum ignorance

## 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 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.