In this public lecture, we discuss how quantum information is more like apples than oranges, and how this translates to a method for unforgeable money and ultra-secure communications. We then link this to quantum interactive proofs, the study of which have recently led to the unravelling of a 50-year old mathematical puzzle called the Connes embedding problem. Finally, we present boson sampling as the first ever demonstration of a computational advantage of quantum computers over conventional ones.

This public lecture is dedicated to first-year undergraduate students who often ask: “what good is linear algebra?”. My goal is to make this talk accessible to you, and to provide you with some answers to this very good question! 😊