That important exam is in a few hours and not only has Bob not studied for it, he can’t remember any of the material from the course. Quickly he asks Alice, a more responsible student, to give him her notes to go through. Not wanting Bob to get a free pass on this exam, Alice only gives him notes on half the material, so every question relating to the other half he can only guess at. To make things even worse, the examiner has seen the cheat sheet and has made questions it does not cover, specifically to trap Bob in his ignorance. Obviously Bob will fail the test… right? Not if those notes contain quantum information, as opposed to classical. Add this to the list of weird quantum mechanical phenomena.
Physicists at the Center for Quantum Technologies at the National University of Singapore have found quantum ignorance is far from intuitive. If Bob, with half of the information of the course, is asked questions only on one half or less of the course, he can still pass, even if the examiner saw the notes. If the questions cover more than half of the information, then Bob will not be able to answer those questions correctly. The researchers have already devised an experiment to test Bob on just over half the information and are working on other ways to explore this effect that may have profound impact on quantum cryptography and computing.