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

Carlos Galindo; Fernando Hernando; Ryutaro Yamashita; Diego Ruano

doi:10.1007/s11128-019-2234-5

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

Carlos Galindo, Fernando Hernando, Ryutaro Yamashita, Diego Ruano

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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.

Original language	English
Article number	116
Journal	Quantum Information Processing
Volume	18
Issue number	4
ISSN	1570-0755
DOIs	https://doi.org/10.1007/s11128-019-2234-5
Publication status	Published - 2019

Keywords

Entanglement-assisted quantum error-correcting codes
Gilbert–Varshamov bound
Symplectic, Hermitian and Euclidean duality

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10.1007/s11128-019-2234-5

Galindo2019_Article_Entanglement-assistedQuantumErFinal published version, 342 KBLicence: CC BY 4.0

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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.",

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AU - Galindo, Carlos

AU - Hernando, Fernando

AU - Yamashita, Ryutaro

AU - Ruano, Diego

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Entanglement-assisted quantum error-correcting codes

KW - Gilbert–Varshamov bound

KW - Symplectic, Hermitian and Euclidean duality

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U2 - 10.1007/s11128-019-2234-5

DO - 10.1007/s11128-019-2234-5

M3 - Journal article

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VL - 18

JO - Quantum Information Processing

JF - Quantum Information Processing

IS - 4

M1 - 116

ER -

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

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Keywords

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