Constructions of $\ell$-Adic $t$-Deletion-Correcting Quantum Codes

Abstract

We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad. The second one corrects multiple deletions and can construct asymptotically good codes. The second one also allows conversion of stabilizer-based quantum codes to deletion-correcting codes, and entanglement assistance.

LaTeX2e, 6 pages, no figure, version 2 only corrects typos

References in corpus (3)

• Correcting Quantum Errors with Entanglement
• Permutation-invariant quantum coding for quantum deletion channels
• Permutation-Invariant Quantum Codes for Deletion Errors