  We study the relative entanglement entropies of one interval between excited
states of a 1+1 dimensional conformal field theory (CFT). To compute the
relative entropy $S(\rho_1 \| \rho_0)$ between two given reduced density
matrices $\rho_1$ and $\rho_0$ of a quantum field theory, we employ the replica
trick which relies on the path integral representation of ${\rm Tr} ( \rho_1
\rho_0^{n-1} )$ and define a set of R\'enyi relative entropies $S_n(\rho_1 \|
\rho_0)$. We compute these quantities for integer values of the parameter $n$
and derive via the replica limit, the relative entropy between excited states
generated by primary fields of a free massless bosonic field. In particular, we
provide the relative entanglement entropy of the state described by the primary
operator $i \partial\phi$, both with respect to the ground state and to the
state generated by chiral vertex operators. These predictions are tested
against exact numerical calculations in the XX spin-chain finding perfect
agreement.
