  We study the entanglement of purification (EoP) of subsystem $A$ and B in
conformal field theories (CFTs) stressing on its relation to unitary operations
of disentanglement, if the auxiliary subsystem $\tilde{A}$ adjoins $A$ and
$\tilde{A}\tilde{B}$ is the complement of $AB$. We estimate the amount of the
disentanglement by using the holographic EoP conjecture as well as the
inequality of Von Neumann entropy. Denote the state that produces the EoP by
$|\psi\rangle_M$. We calculate the variance of entanglement entropy of
$A\tilde{A}$ in the state $|\psi(\delta)\rangle:=e^{i\delta
H_{\tilde{A}\tilde{B}}}|\psi\rangle_M$. We find a constraint on the state
$|\psi\rangle_M$, $[K_{A\tilde{A},M},O_{\tilde{A}}]=0$, where
$K_{A\tilde{A},M}$ is the modular Hamiltonian of $A\tilde{A}$ in the state
$|\psi\rangle_M$, $O_{\tilde{A}}\in \mathscr{R}(\tilde{A})$ is an arbitrary
operator. We also study three different states that can be seen as disentangled
states. Two of them can produce the holographic EoP result in some limit. But
we show that none of they could be a candidate of the state $|\psi\rangle_M$,
since the distance between these three states and $|\psi\rangle_M$ is very
large.
