The Hamming distances of saturated asymmetrical orthogonal arrays with strength 2

Pang, Shanqi; Zhang, Xiao; Zhang, Qingjuan

doi:10.1080/03610926.2019.1591452

Cited by 12 publications

(5 citation statements)

References 21 publications

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“…0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 (1) We have HD(L) = 6, 7 by Ref. [21]. Then we can obtain an IrMOA(16, m + 2, 4 2 2 m , 2) for 6 ≤ m ≤ 9 by Lemma 1.…”

Section: Resultsmentioning

confidence: 91%

Quantum Frequency Arrangements, Quantum Mixed Orthogonal Arrays and Entangled States

Pang

Zhang

Xiao

2020

IEICE Trans. Fundamentals

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In this work, we introduce notions of quantum frequency arrangements consisting of quantum frequency squares, cubes, hypercubes and a notion of orthogonality between them. We also propose a notion of quantum mixed orthogonal array (QMOA). By using irredundant mixed orthogonal array proposed by Goyeneche et al. we can obtain k-uniform states of heterogeneous systems from quantum frequency arrangements and QMOAs. Furthermore, some examples are presented to illustrate our method.

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Section: Resultsmentioning

confidence: 91%

Quantum Frequency Arrangements, Quantum Mixed Orthogonal Arrays and Entangled States

Pang

Zhang

Xiao

2020

IEICE Trans. Fundamentals

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“…As is often the case, OAs can be very useful for quantum information theory [22,41,42,43]. Recently, many new construction methods of MOAs with high strength have been provided [44,45,46,47,48,49,50,51,52,53,54]. Such new developments in MOAs make it possible to obtain infinitely many new k-uniform states in heterogeneous systems from IrMOAs.…”

Section: Introductionmentioning

confidence: 96%

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

Pang,

Zhang,

Fei

et al. 2021

Preprint

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Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (OAs) to heterogeneous multipartite systems with different individual levels. The second is the existence of k-uniform states in heterogeneous quantum systems. We present explicit constructions of two and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels, and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of k-uniform states for heterogeneous multipartite systems for any k ≥ 2. The non-existence of a class of IrMOAs is also proved.

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“…As is often the case, they can be useful for quantum information theory. In recent years, many new classes of OAs, especially high strength OAs have been obtained [42][43][44][45][46][47]. The relationship among OAs, CECCs, quantum uniform states and QECCs was further revealed [30,36,[48][49][50][51][52]].…”

Section: Introductionmentioning

confidence: 99%

Near MDS and near quantum MDS codes via orthogonal arrays

Pang,

Zhang,

Chen

et al. 2024

Quantum Sci. Technol.

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Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using symmetrical orthogonal arrays (OAs), we construct a lot of NMDS, $m$-MDS and almost extremal NMDS codes. Quantum error-correcting codes (QECCs) play a central role in quantum information processing and can protect quantum information from various quantum noises. We present a general method for constructing QECCs over mixed alphabets through asymmetrical OAs. Since quantum maximum distance separable (QMDS) codes over mixed alphabets with the dimension equal to one have not been found in all the literature so far, the definition of a near quantum maximum distance separable (NQMDS) code over mixed alphabets is proposed. By using asymmetrical OAs, we obtain many such codes.

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The Hamming distances of saturated asymmetrical orthogonal arrays with strength 2

Cited by 12 publications

References 21 publications

Quantum Frequency Arrangements, Quantum Mixed Orthogonal Arrays and Entangled States

Quantum Frequency Arrangements, Quantum Mixed Orthogonal Arrays and Entangled States

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

Near MDS and near quantum MDS codes via orthogonal arrays

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