SEMINAR 2023

Measurements are one of the most fundamental yet enigmatic aspects of quantum mechanics. When a quantum system is measured, not only do we gain information, but also the state of the system is inevitably altered. With the emergence of quantum simulators and computers of increasing size and controllability, a great deal of theoretical work has gone into understanding how measurements can influence the dynamics of many-body quantum systems, and potentially even be used as a resource for their control. However, in implementing such schemes in practice, an intrinsic obstacle can arise related to how much knowledge we can in principle possess about the post-measurement state – an issue known as the “postelection problem”. In this talk, I will introduce the fundamentals of measurement-induced dynamics and explain why this problem arises. I will then discuss to what extent this issue can in principle be circumvented using methods from the fields of statistical inference and convex optimization. These results reveal a fundamental distinction between quantities that can or cannot be learned about quantum systems undergoing measurements, and point to limitations and opportunities for future quantum information technologies.