  We study entanglement via the subsystem purity relative to bipartitions of
arbitrary excited states in (1+1)-dimensional conformal field theory,
equivalent to the scaling limit of one dimensional quantum critical systems. We
compute the exact subpurity as a function of the relative subsystem size for
numerous excited states in the Ising and three-state Potts models. We find that
it decays exponentially when the system and the subsystem sizes are comparable
until a saturation limit is reached near half-partitioning, signaling that
excited states are maximally entangled. The exponential behavior translates
into extensivity for the second R\'enyi entropy. Since the coefficient of this
linear law depends only on the excitation energy, this result shows an
interesting, new relationship between energy and quantum information and
elucidates the role of microscopic details.
