  The AdS/CFT correspondence is an explicit realization of the holographic
principle relating a theory of gravity in a volume of space to a lower
dimensional quantum field theory on its boundary. By exploiting elements of
quantum error correction, qubit toy models of this correspondence have been
constructed for which the bulk logical operators are representable by operators
acting on the boundary. Given a boundary subregion, wedges in the volume space
are used to enclose the bulk qubits for which logical operators are
reconstructable on that boundary subregion. In this thesis a number of
different wedges, such as the causal wedge, greedy entanglement wedge and
minimum entanglement wedge, are examined. More specifically, Monte-Carlo
simulations of boundary erasure are performed with various toy models to study
the differences between wedges and the effect on these wedge by the type of the
model, non-uniform boundaries and stacking of models. It has been found that
the minimum entanglement wedge is the best approximate for the true geometric
wedge. This is illustrated by an example toy model for which an operator beyond
the greedy entanglement wedge was also reconstructed. In addition, by
calculating the entropy of these subregions, the viability of a mutual
information wedge is rejected. Only for particular connected boundary
subregions was the inclusion of the central tensor by the geometric wedge
associated to a rise in mutual information.
