  We study real-space quantum entanglement included in conformally invariant
boundary states in conformal field theories (CFTs). First, we argue that
boundary states essentially have no real-space entanglement by computing the
entanglement entropy when we bipartite the system into two spatial regions.
From the viewpoint of holography, this shows that boundary states are dual to
trivial spacetimes of zero spactime volume. Next, we point out that a
continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs
can be formulated by employing a boundary state as its infrared unentangled
state with an appropriate regularization. Exploiting this idea, we propose an
approximation scheme of cMERA construction for general CFTs.
