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.