Entanglement entropy and negative energy in two dimensions

It is well known that quantum effects can produce negative energy densities, though for limited times. Here we show in the context of two-dimensional conformal field theory that such negative energy densities are present in any nontrivial conformal vacuum and can be interpreted in terms of the entanglement structure of such states. We derive an exact identity relating the outgoing energy flux and the entanglement entropy in the in-vacuum. When applied to two-dimensional models of black hole evaporation, this identity implies that unitarity is incompatible with monotonic mass loss.