An entropy bound due to symmetries

Abstract

Let [Formula: see text] be a local net of real Hilbert subspaces of a complex Hilbert space [Formula: see text] on the family [Formula: see text] of double cones of the spacetime [Formula: see text] ([Formula: see text] odd), covariant with respect to a positive energy, unitary representation [Formula: see text] of the Poincaré group [Formula: see text], with the Bisognano–Wichmann property for the wedge modular group. We set an upper bound on the local entropy [Formula: see text] of a vector [Formula: see text] in a given region [Formula: see text] that depends only on [Formula: see text] and the PCT anti-unitary canonically associated with [Formula: see text]. A similar result holds for local, Möbius covariant nets of standard subspaces on the circle. We compute the entropy increase with respect to the dual net and illustrate this bound for the nets associated with the [Formula: see text]-current derivatives.