Quantum error correction on infinite-dimensional Hilbert spaces

Understand

We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces.

• The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts.
• The error correction theory we develop begins with a shift of focus from states to algebras of observables.
• Standard subspace codes and subsystem codes are seen as the special case of algebras of observables given by finite-dimensional von Neumann factors of type I.