A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory

Abstract

We numerically investigate the Araki-Uhlmann relative entropy in Quantum Field Theory, focusing on a free massive scalar field in $1+1$-dimensional Minkowski spacetime. Using Tomita-Takesaki modular theory, we analyze the relative entropy between a coherent state and the vacuum state, with several types of test functions localized in the right Rindler wedge. Our results confirm that relative entropy decreases with increasing mass and grows with the size of the spacetime region, aligning with theoretical expectations.