  In this paper, we study the bulk local states in AdS/CFT correspondence in
the large $N$ limit using the formula explicitly relating the bulk local
operators and the CFT local operators. We identify the bulk local state in
terms of CFT local states and find that the bulk local state corresponds to a
CFT state supported in the whole space, which means a version of the subregion
duality is not valid. On the other hand, CFT states supported in a space region
are expressed in terms of the bulk states supported in a certain region. We
find that the quantum error correction proposal is not realized although the
puzzles of the radial locality which motivated the proposal are resolved in our
analysis. For the understating of the bulk local states, an explicit
realization of an analogue of the Reeh-Schlieder theorem plays an important
role.
