Fig. 5: Bulk reconstruction in HTN codes.
a For perfect tensors, any index bipartition into regions A and Ac leads to a reconstruction of the logical index (red dot) on either A or Ac. b For the non-perfect tensors used in the HTN code, bipartitions exist for which neither A nor Ac are sufficient for reconstruction. c For a patch of the {5, 4} ququart HTN code with \({A}^{{\prime} }\) and B tensors given by (9) and (12), we can show state-dependent reconstruction explicitly: For the given boundary regions A and Ac, the central bulk ququart cannot be state-independently reconstructed on either. But given local projections of the neighboring bulk ququart on eigenstates of the logical ququart Paulis \(\bar{X}\) and \(\bar{Z}\), it can be fully reconstructed on either A or Ac. While the RT surface γA bounding the reconstructible region changes, its length ∣γA∣ remains constant.
