Constraints on robust quantum information storage

In, the authors derive a bound on the density of quantum information which can be reliably encoded in a finite region of Euclidean space. While all evidence suggests that the local geometry of the universe is approximately Euclidean, it is possible to embed surfaces with hyperbolic geometries into Euclidean space. Furthermore, it has been demonstrated that quantum error correcting codes
derived from cellulations of hyperbolic surfaces have desirable properties, exceeding their Euclidean counterparts. This motivates the search for a similar bound in hyperbolic space. This avenue of
investigation may be extended into an analogous result for approximate error correction, as in, or generalised to gain insight into the relationship between dimensionality and limits on information
storage density.