Bekenstein bound for approximately local charged states

Source abstract

In this paper, we generalize the energy-entropy ratio inequality in quantum field theory (QFT) established by one of us from localized states to a larger class of states. The states considered in this paper can be in a charged (non-vacuum) representation of the QFT or may be only approximately localized in the region under consideration. Our inequality is [Formula: see text], where S is the relative entropy, where R is a “radius” (width) characterizing the size of the region, [Formula: see text] is the statistical (quantum) dimension of the given charged sector [Formula: see text] hosting the quantum state [Formula: see text], [Formula: see text] is the vacuum state, [Formula: see text] is the Hamiltonian in the charged sector, and [Formula: see text] is a tolerance measuring the deviation of [Formula: see text] from the vacuum according to observers in the causal complement of the region.