  We investigate entanglement of purification in conformal field theory. By
using Reeh-Schlieder theorem, we construct a set of the purification states for
$\rho_{AB}$, where $\rho_{AB}$ is reduced density matrix for subregion $AB$ of
a global state $\rho$. The set can be approximated by acting all the unitary
observables,located in the complement of subregion $AB$, on the global state
$\rho$, as long as the global state $\rho$ is \text{cyclic} for every local
algebra, e.g., the vacuum state. Combining with the gravity explanation of
unitary operations in the context of the so-called surface/state
correspondence, we prove the holographic EoP formula. We also explore the
projective measurement with the conformal basis in conformal field theory and
its relation to the minimization procedure of EoP. Interestingly, though the
projective measurement is not a unitary operator, the difference in some limits
between holographic EoP and the entanglement entropy after a suitable
projective measurement is a constant $\frac{c}{3}\log 2$ up to some
contributions from boundary. This suggests the states after projective
measurements may approximately be taken as the purification state corresponding
to the minimal value of the procedure.
