The Quantum Hamming Bound in Arbitrary Local Dimension
This work proves that the quantum Hamming bound holds for exact quantum error correction codes regardless of their local dimension. The authors address degeneracy, where distinct physical errors might act identically on a code subspace, by reframing it as a collision between two correctable balls. They establish bounds for high-alphabet systems and specifically verify the nonbinary case (qutrits), confirming that degeneracy cannot overcome the fundamental Hamming inequality.