Entanglement-assisted operator codeword stabilized quantum codes

Jeonghwan Shin, Jun Heo, Todd A. Brun

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes (QECCs), including additive and nonadditive codes, based on the codeword stabilized (CWS) framework on subsystems. The CWS framework is a scheme to construct QECCs, including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct QECCs. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes

Original languageEnglish
Pages (from-to)1921-1936
Number of pages16
JournalQuantum Information Processing
Volume15
Issue number5
DOIs
Publication statusPublished - 2016 May 1

Keywords

  • Codeword stabilized quantum codes
  • Entanglement-assisted quantum error-correcting codes
  • Operator quantum error-correcting codes
  • Quantum error correction
  • Quantum information

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering

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