A new way to map quantum codes reveals how errors are corrected

Enrico Bozzetto of Politecnico di Torino and Newcastle University and Jonte R. Hance of Newcastle University have established a new connection between mathematical quasiprobability representations and quantum error correction. Their work demonstrates that a phase-space representation of a quantum code is possible only when the code space satisfies specific conditions. The researchers found that only the Gottesman-Kitaev-Preskill family meets these criteria, revealing limitations in the design of certain quantum codes. The study also links a property in qudit stabiliser codes, for those with odd prime dimensions, directly to a quantum resource. The structure of quantum error correction is directly linked to quasiprobability representations, enabling a new method for determining how error channels impact…