Relative entropic uncertainty relation for scalar quantum fields

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 straightforward generalization to quantum field theories. In this work, we overcome this difficulty by introducing the notion of a functional relative entropy and show that it has a meaningful field theory limit. We present the first entropic uncertainty relation for a scalar quantum field theory and exemplify its behavior by considering few particle excitations and the thermal state. Also, we show that the relation implies the multidimensional Heisenberg uncertainty relation.

Automated summary

The concept of entropic uncertainty is well-known for formulating uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. In this work, the introduction of functional relative entropy overcomes the difficulty of scaling bounds with the number of oscillator modes in quantum field theories. The first entropic uncertainty relation for a scalar quantum field theory is presented, and it is shown to imply the multidimensional Heisenberg uncertainty relation.