Hiding Ignorance and Finding Knowledge: Adventures Using the Shape of Light

Abstract: The transverse shape of light has emerged in recent years as a promising platform for encoding quantum information, for the multiple levels that it affords and the ease with which shape can be controlled. To demonstrate, I will discuss two recent experiments. The first is on ignorance: One might ask if ignorance of a whole system implies 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. I will give an experimental evidence that supports this counterintuitive fact. The second is on learning: We used a tomographic technique inspired by machine learning to track a quantum state as the state changes. The method is computationally efficient and also robust—it converges to a good estimate even in the presence of strong noise. Developing techniques like this is especially important for systems that are of high dimensionality, where making tomographically complete measurements become impractical.