Non-binary entanglement-assisted quantum stabilizer codes

Luo, Liang; Ma, Zhi; Wei, Zhengchao; Riguang, Leng

doi:10.1007/s11432-015-0932-y

Cited by 22 publications

(26 citation statements)

References 22 publications

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“…Our purpose in this section is to determine the optimal required number of pairs of maximally entangled states of the EAQECC over an arbitrary finite field F q that can be constructed from an F q -linear code C ⊆ F 2n q with dimension n − k. Assume that (H X |H Z ) is an (n − k) × 2n generator matrix of C. The case when m = 1 (i.e., q is prime) is known (see [26,18]) and the corresponding result is the following:…”

Section: Eaqeccs Over F Qmentioning

confidence: 99%

“…In fact, [26] proves that the optimal number c of ebits required for a binary entanglement-assisted quantum error-correcting code with generator matrix (H X |H Z ) is rank(H X H T Z − H Z H T X )/2, where the superindex T means transpose. Remark 1 in that paper states, without a proof, that the same formula holds when considering codes over finite fields F p , p being a prime number, a proof can be found in [18].…”

Section: Introductionmentioning

confidence: 97%

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

Galindo

Hernando

Matsumoto

et al. 2019

Quantum Inf Process

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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.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

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Section: Eaqeccs Over F Qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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

Galindo

Hernando

Matsumoto

et al. 2019

Quantum Inf Process

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“…In the binary case the construction of these codes is described in [26] (third paragraph of Section II). This construction also holds for codes over finite fields of the type F p , p being a prime number (see [44, Remark 1] and [34] for a proof). There it is proved that one can obtain an EAQECC from a classical code C ⊆ F 2n p such that C ⊆ C ⊥ts and the set of detectable quantum errors is given by…”

Section: Asymmetric Eaqeccsmentioning

confidence: 99%

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

et al. 2020

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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.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

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“…This EA framework provides the power to construct quantum codes from any group of quantum operators operating over the qudits leading to the construction of codes with better error correction capability [10]. All known quantum error correction codes based on finite fields [2] [5] [6] [11] [12] are special cases of this construction. Using the proposed framework in [10], quantum codes can be constructed from well-known classical codes, such as Reed-Solomon (RS) codes [13], etc.…”

Section: Introductionmentioning

confidence: 99%

“…Existing encoding procedures for entanglement-assisted stabilizer codes over qudits of dimension p (prime p) and qubits provided in [11] and [16], respectively, are special cases of the work proposed in this paper. In [15], Grassl et al proposed the encoding procedure for entanglementunassisted qudit stabilizer codes that correspond to classical linear codes.…”

Section: Introductionmentioning

confidence: 99%

Encoding of Nonbinary Entanglement-Unassisted and Assisted Stabilizer Codes

Nadkarni

Garani

2021

IEEE Trans. Quantum Eng.

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Quantum coding schemes over qudits using pre-shared entanglement between the encoder and decoder can provide better error correction capability than without it. In this paper, we develop procedures for constructing encoding operators for entanglement-unassisted and entanglement-assisted qudit stabilizer codes over F p k , with p prime and k ≥ 1 from first principles, generalizing prior works on qubit based codes and codes that work over F p . We also provide quantum encoding architectures based on the proposed encoding procedures using one and two qudit gates, useful towards realizing coded quantum computing and communication systems using qudits.INDEX TERMS Quantum error correction, Entanglement-assisted codes, Encoding architecture, Qudit stabilizer codes, Non-binary codes. 1 The encoding circuit complexity linearly increases with codelength. To realize the practical implementation of large length codes, we need to construct all the stabilizers or their extensions from a carefully chosen group of quantum operators, making it a computationally challenging problem.2 Preliminary version on the encoding procedure for entanglementunassisted stabilizer codes over qudits was presented at IEEE Globecom 2018, Abu Dhabi [14].

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Non-binary entanglement-assisted quantum stabilizer codes

Cited by 22 publications

References 22 publications

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

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

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

Encoding of Nonbinary Entanglement-Unassisted and Assisted Stabilizer Codes

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