Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator modes, preventing a straight-forward generalization to quantum field theories. In this talk, we will present a way of overcoming this difficulty by introducing the notion of a functional relative entropy, which has a meaningful field theory limit. We will show the first entropic uncertainty relation for a scalar quantum field theory and illustrate that its bound remains finite also for an infinite number of oscillator modes.
ArXiv reference: https://arxiv.org/abs/2107.07824