Asymmetric entanglement-assisted quantum codes: bound and constructions

Liu, Hualu; Peng, Hu; Liu, Xiusheng

doi:10.1007/s10623-021-00845-z

Cited by 5 publications

(12 citation statements)

References 24 publications

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“…The decomposition method of the defining set of constacyclic codes is re-characterized and applied to construct asymmetric EAQMDS codes. Under the same code length and fixed d z and d x , some asymmetric EAQMDS codes constructed in this paper can achieve the same net rate (k − c)/n as the quantum codes in [18]. However, the asymmetric EAQMDS codes in this paper require fewer entangled states, which means that the preparation cost and cost of quantum entangled states required in this paper are less.…”

mentioning

confidence: 90%

“…Recently, Galindo et al introduced the concept of asymmetric EAQEC codes and presented an explicit computation of the parameters for asymmetric EAQEC codes derived from BCH codes [16]. Moreover, the quantum Singleton bound for asymmetric EAQMDS codes has been established in [16][17][18][19], along with the proposal of a general Euclidean construction method based on cyclic codes. Although there has been some progress in the study of asymmetric EAQMDS codes, several issues still need to be addressed.…”

Section: Introductionmentioning

confidence: 99%

“…However, the asymmetric EAQMDS codes in this paper require fewer entangled states, which means that the preparation cost and cost of quantum entangled states required in this paper are less. In addition, some quantum codes that do not exist in [18,[20][21][22][23][24][25][26][27][28][29] are obtained in this paper. Moreover, the minimum distance d z of some asymmetric EAQMDS codes constructed in this paper is much greater than q, indicating that such quantum codes have greater asymmetric error-correcting ability.…”

mentioning

confidence: 99%

“…, respectively, where the number of entangled states constructed for asymmetric EAQMDS codes is universal. In Section 5, we mainly compare the parameters of the asymmetric EAQMDS codes constructed in this paper with those of the quantum codes in [18,25,27,28]. In Section 6, we present our conclusion and discussion.…”

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confidence: 99%

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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Chen,

Fang,

Zhou

et al. 2023

Entropy

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Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of literature has investigated the construction of asymmetric QEC codes. However, the asymmetry of most QEC codes identified in the literature is limited by the dual-containing condition within the Calderbank-Shor-Steane (CSS) framework. This limitation restricts the exploration of their full potential in terms of asymmetry. In order to enhance the asymmetry of asymmetric QEC codes, we utilize entanglement-assisted technology and exploit the algebraic structure of cyclotomic cosets of constacyclic codes to achieve this goal. In this paper, we generalize the decomposition method of the defining set for constacyclic codes and apply it to count the number of pre-shared entangled states in order to construct four new classes of asymmetric entanglement-assisted quantum maximal-distance separable (EAQMDS) codes that satisfy the asymmetric entanglement-assisted quantum Singleton bound. Compared with the codes existing in the literature, the lengths of the constructed EAQMDS codes and the number of pre-shared entangled states are more general, and the codes constructed in this paper have greater asymmetry.

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confidence: 90%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Chen,

Fang,

Zhou

et al. 2023

Entropy

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“…Then they presented the explicit computation of the parameters of AEAQECCs via BCH codes. Liu et al [13] constructed three new families of AEAQECCs by means of Vandermonde matrices, extended GRS codes and cyclic codes.…”

Section: Introductionmentioning

confidence: 99%

On pure MDS asymmetric entanglement-assisted quantum error-correcting codes

Huang,

Fang,

2021

Preprint

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Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) from Calderbank-Shor-Steane (CSS) construction. In general, it's difficult to determine the required number of maximally entangled states of an AEAQECC, which is associated with the dimension of the intersection of the two corresponding linear codes. Two linear codes are said to be a linear l-intersection pair if their intersection has dimension l. In this paper, all possible linear l-intersection pairs of MDS codes are given. As an application, we give a complete characterization of pure MDS AEAQECCs for all possible parameters.

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Linear ℓ-intersection pairs of MDS codes and their applications to AEAQECCs

Huang

Fang

2022

Cryptogr. Commun.

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Asymmetric entanglement-assisted quantum codes: bound and constructions

Cited by 5 publications

References 24 publications

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

On pure MDS asymmetric entanglement-assisted quantum error-correcting codes

Linear ℓ-intersection pairs of MDS codes and their applications to AEAQECCs

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