Opt for a Quantum Exam Instead

In the quantum world, it seems, knowing a little counts for a lot

Imagine you have studied just a single page of a textbook for an exam. For a teacher, it should be easy to set a question based on information from any one page of the book that you cannot answer. Or so it should be in our world. But it seems the world of quantum theory continues to supply us with results that astonish. In the quantum world, it turns out, knowledge of one particular page of a book should enable you to answer questions from any other page of the book. Weird as this result is, it is best described directly by a National University of Singapore press release: ‘New research in quantum physics has shown that a quantum know-it-all could lack information about a subject as a whole, yet answer almost perfectly any question about the subject’s parts.’ The work is published in Physical Review Letters. “This is something conceptually very weird,” says Stephanie Wehner of the National University of Singapore, who derived the theoretical result with Thomas Vidick at the University of California, Berkeley.

Wehner and Vidick consider a book with two pages, with two quantum players, Alice and Bob, collaborating. ‘Alice reads the book and is allowed to give Bob one page’s worth of information from it. If Bob only has classical information, it is always possible to work out what he doesn’t know. Imagine that Bob is a student trying to cheat in an exam, and the notes from Alice cover half the course. An examiner, having secretly inspected Bob’s crib notes, could set questions that Bob couldn’t answer. The craziness comes if Bob gets one page’s worth of quantum information from Alice. In this case, the researchers show, there is no way to pinpoint what information Bob is missing. Challenge Bob, and he can guess either page of the book almost perfectly. An examiner could not expose Bob’s ignorance even having seen his notes as long as the questions cover no more than half the course—the total amount of information Bob can recount cannot exceed the size of his notes.’

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