  We develop new techniques for studying the modular and the relative modular
flows of general excited states. We show that the class of states obtained by
acting on the vacuum (or any cyclic and separating state) with invertible
operators from the algebra of a region is dense in the Hilbert space. This
enables us to express the modular and the relative modular operators, as well
as the relative entropies of generic excited states in terms of the vacuum
modular operator and the operator that creates the state. In particular, the
modular and the relative modular flows of any state can be expanded in terms of
the modular flow of operators in vacuum. We illustrate the formalism with
simple examples including states close to the vacuum, and coherent and squeezed
states in generalized free field theory.
