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.

arXiv commentLaTeX2e, 6 pages, no figure, version 2 only corrects typos

References in corpus (10)

• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Error Correction and Orthogonal Geometry
• Correcting Quantum Errors with Entanglement
• Codes for the Quantum Erasure Channel
• Capacities of Quantum Erasure Channels
• Permutation-invariant quantum codes
• Quantum Secret Sharing Schemes and Reversibility of Quantum Operations
• Permutation-invariant quantum coding for quantum deletion channels
• Unitary Reconstruction of Secret for Stabilizer Based Quantum Secret Sharing
• Permutation-Invariant Quantum Codes for Deletion Errors