  We present a new method of deriving shapes of entanglement wedges directly
from CFT calculations. We point out that a reduced density matrix in
holographic CFTs possesses a sharp wedge structure such that inside the wedge
we can distinguish two local excitations, while outside we cannot. We can
determine this wedge, which we call a CFT wedge, by computing a
distinguishability measure. We find that CFT wedges defined by the fidelity or
Bures distance as a distinguishability measure, coincide perfectly with shadows
of entanglement wedges in AdS/CFT. We confirm this agreement between CFT wedges
and entanglement wedges for two dimensional holographic CFTs where the
subsystem is chosen to be an interval or double intervals, as well as higher
dimensional CFTs with a round ball subsystem. On the other hand if we consider
a free scalar CFT, we find that there are no sharp CFT wedges. This shows that
sharp entanglement wedges emerge only for holographic CFTs owing to the large N
factorization. We also generalize our analysis to a time-dependent example and
to a holographic boundary conformal field theory (AdS/BCFT). Finally we study
other distinguishability measures to define CFT wedges. We observe that some of
measures lead to CFT wedges which slightly deviate from the entanglement wedges
in AdS/CFT and we give a heuristic explanation for this. This paper is an
extended version of our earlier letter arXiv:1908.09939 and includes various
new observations and examples.
