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Paper 1
Near MDS and near quantum MDS codes via orthogonal arrays
Shanqi Pang, Chaomeng Zhang, Mengqian Chen, Miaomiao Zhang
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2308.00406
- arXiv
- 2308.00406
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. We establish a relation between asymmetrical OAs and quantum error correcting codes (QECCs) over mixed alphabets. 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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Structured Negativity: A physically realizable measure of entanglement based on structural physical approximation
Anu Kumari, Satyabrata Adhikari
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.03909
- arXiv
- 2209.03909
Quantification of entanglement is one of the most important problem in quantum information theory. In this work, we will study this problem by defining a physically realizable measure of entanglement for any arbitrary dimensional bipartite system $ρ$, which we named as structured negativity $(N_S(ρ))$. We have shown that the introduced measure satisfies the properties of a valid entanglement monotone. We also have established an inequality that relate negativity and the structured negativity. For $d\otimes d$ dimensional state, we conjecture from the result obtained in this work that negativity coincide with the structured negativity when the number of negative eigenvalues of the partially transposed matrix is equal to $\frac{d(d-1)}{2}$. Moreover, we proved that the structured negativity not only implementable in the laboratory but also a better measure of entanglement in comparison to negativity. In few cases, we obtain that structure negativity gives better result than the lower bound of the concurrence obtained by Albeverio [Phys. Rev. Lett. \textbf{95}, 040504 (2005)].
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