A Bekenstein-Type Bound in QFT

Let B be a spacetime region of width 2R>0, and phi a vector state localized in B. We show that the vacuum relative entropy of phi, on the local von Neumann algebra of B, is bounded by 2 pi R-times the energy of the state phi in B. This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.