Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.03079 · Computational and Applied Mathematics

Steane enlargement of entanglement-assisted quantum error-correcting codes

Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto

Published Aug 7, 2023• 0 citations
arXivHTMLPDF

Abstract

Abstract We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our results to explicitly compute the parameters of enlarged EAQECCs coming from some BCH codes.

DOI
10.1007/s40314-023-02410-x

Related papers

Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes

Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto +1 more

The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is presented. Explicit parameters of asymmetric EAQECCs from BCH codes are computed and examples exceeding the introduced Gilbert-Varshamov bound are shown.

arXiv:1911.10031•IEEE Access•Jan 1, 2020•28 citations

Maximal entanglement entanglement-assisted quantum codes from quaternary BCH codes

Liangdong Lv, Ruihu Li, Qiang Fu +1 more

Maximal entanglement entanglement-assisted quantum error correcting codes (EAQECCs) can achieve the EA-hashing bound asymptotically, and a higher rate and/or better noise suppression capabilities may be achieved by exploiting maximal entanglement. In this work, we discuss construction of some families of [n, k, d] zero radical codes with minimal distance d ≥ 6, 8, 10, 12, 14 from two classes of quaternary Bose-Chaudhuri-Hocquenghem (BCH) codes. Using these zero radical codes, we construct many maximal entanglement EAQECCs with very good parameters. We calculate the parameters of these EAQECCs by easily algebraical method, rather than by usually method of computation by computer. The maximal entanglement EAQECCs presented here have better parameters than those available in the literature.

IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC)•Dec 1, 2015•7 citations

An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve

René Bødker Christensen, Carlos Munuera, Francisco Revson F. Pereira +2 more

We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $ c $, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing $ c $ for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.

arXiv:2105.02166•Advances in Mathematics of Communications•Jan 12, 2022•2 citations

General entanglement-assisted quantum error-correcting codes

Min-Hsiu Hsieh, Igor Devetak, Todd A. Brun

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs, which can only be constructed from dual-containing codes. Operator quantum error-correcting codes allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error-correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.

arXiv:0708.2142•Physical Review A•Dec 19, 2007•131 citations

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto +1 more

Abstract We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert–Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.

arXiv:1812.05312•Quantum Information Processing•Mar 4, 2019•108 citations

General entanglement-assisted quantum error-correcting codes

Todd A. Brun, Igor Devetak, Min-Hsiu Hsieh

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement- assisted quantum error correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2007•25 citations
Abstract We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our results to explicitly compute the parameters of enlarged EAQECCs coming from some BCH codes.
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is presented. Explicit parameters of asymmetric EAQECCs from BCH codes are computed and examples exceeding the introduced Gilbert-Varshamov bound are shown.
Maximal entanglement entanglement-assisted quantum error correcting codes (EAQECCs) can achieve the EA-hashing bound asymptotically, and a higher rate and/or better noise suppression capabilities may be achieved by exploiting maximal entanglement. In this work, we discuss construction of some families of [n, k, d] zero radical codes with minimal distance d ≥ 6, 8, 10, 12, 14 from two classes of quaternary Bose-Chaudhuri-Hocquenghem (BCH) codes. Using these zero radical codes, we construct many maximal entanglement EAQECCs with very good parameters. We calculate the parameters of these EAQECCs by easily algebraical method, rather than by usually method of computation by computer. The maximal entanglement EAQECCs presented here have better parameters than those available in the literature.
We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $ c $, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing $ c $ for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs, which can only be constructed from dual-containing codes. Operator quantum error-correcting codes allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error-correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement- assisted quantum error correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.