Holographic Quantum Error-Correcting Codes

Bulk logical operators encoded redundantly into boundary quantum degrees of freedom. The main concepts are entanglement wedge, RT, operator reconstruction. Each must be defined in the context of a concrete physical model, mathematical representation, or experimental task. Terminology alone does not establish the behavior of the system.

In holographic duality, a family of boundary states can represent a restricted bulk code subspace. Certain bulk operators admit reconstruction on more than one boundary region, analogous to logical observables in error correction. Entanglement-wedge reconstruction and complementary recovery depend on code-subspace restrictions and the semiclassical regime; they do not prove a generic laboratory quantum code literally generates a gravitational universe.

Develop a finite-dimensional tensor-network toy model and identify its logical algebra, erasure-correctable boundary regions and entanglement entropies. Calculate where bulk reconstruction succeeds and fails as the boundary region changes. Compare the area-law network model against assumptions needed for actual gravitational Ryu–Takayanagi behavior.