  We study the relative entropy and the trace square distance, both of which
measure the distance between reduced density matrices of two excited states in
two dimensional conformal field theories. We find a general formula for the
relative entropy between two primary states with the same conformal dimension
in the limit of a single small interval and find that in this case the relative
entropy is proportional to the trace square distance. We check our general
formulae by calculating the relative entropy between two generalized free
fields and the trace square distance between the spin and disorder operators of
the critical Ising model. We also give the leading term of the relative entropy
in the small interval expansion when the two operators have different conformal
dimensions. This turns out to be universal when the CFT has no primaires
lighter than the stress tensor. The result reproduces the previously known
special cases.
