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 language | English |
|---|---|
| Pages (from-to) | 1-16 |
| Number of pages | 16 |
| Journal | Quantum Information Processing |
| DOIs | |
| Publication status | Accepted/In press - 2016 Jan 12 |
Fingerprint
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
- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials
- Statistical and Nonlinear Physics
- Signal Processing
- Modelling and Simulation
- Theoretical Computer Science
Cite this
Entanglement-assisted operator codeword stabilized quantum codes. / Shin, Jeonghwan; Heo, Jun; Brun, Todd A.
In: Quantum Information Processing, 12.01.2016, p. 1-16.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Entanglement-assisted operator codeword stabilized quantum codes
AU - Shin, Jeonghwan
AU - Heo, Jun
AU - Brun, Todd A.
PY - 2016/1/12
Y1 - 2016/1/12
N2 - 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
AB - 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
KW - Codeword stabilized quantum codes
KW - Entanglement-assisted quantum error-correcting codes
KW - Operator quantum error-correcting codes
KW - Quantum error correction
KW - Quantum information
UR - http://www.scopus.com/inward/record.url?scp=84954327990&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84954327990&partnerID=8YFLogxK
U2 - 10.1007/s11128-015-1235-2
DO - 10.1007/s11128-015-1235-2
M3 - Article
SP - 1
EP - 16
JO - Quantum Information Processing
JF - Quantum Information Processing
SN - 1570-0755
ER -