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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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Entanglement at the interplay between single- and many-bodyness
Jose Reslen
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.04287
- arXiv
- 2209.04287
The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and many-bodyness. In systems of two fermions, tensor networks describing ground states of interacting Hamiltonians cannot be written as a sequence of next-neighbor unitaries applied on an uncorrelated state, but need four-next-neighbor unitaries in addition. This differs from the idea that the ground state can be obtained as a sequence of next-neighbor operations applied on a tensor network. The work uncovers the transcendence of the notion of many-bodyness in the implementation of protocols based on matrix product states.
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