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The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability…

Quantum Physics · Physics 2012-09-26 Ching-Yi Lai , Todd A. Brun

In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs)…

Information Theory · Computer Science 2021-03-23 Jihao Fan , Jun Li , Jianxin Wang , Zhihui Wei , Min-Hsiu Hsieh

We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional…

Quantum Physics · Physics 2022-02-04 Todd Brun , Igor Devetak , Min-Hsiu Hsieh

Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…

Information Theory · Computer Science 2020-09-08 Jingjie Lv , Ruihu Li , Yu Yao

The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…

Quantum Physics · Physics 2024-06-18 Shanqi Pang , Mengqian Chen , Rong Yan , Yan Zhu

Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…

Quantum Physics · Physics 2011-04-27 Yuichiro Fujiwara , Min-Hsiu Hsieh

In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It…

Information Theory · Computer Science 2019-12-09 Weijun Fang , Fang-Wei Fu , Lanqiang Li , Shixin Zhu

Entanglement-assisted classical communication (EACC) aims to enhance communication systems using entanglement as an additional resource. However, there is a scarcity of explicit protocols designed for finite transmission scenarios, which…

Quantum Physics · Physics 2025-02-04 Tushita Prasad , Markus Grassl

This paper proposes new propagation rules on quantum codes in the entanglement-assisted and in quantum subsystem scenarios. The rules lead to new families of such quantum codes whose parameters are demonstrably optimal. To obtain the…

Information Theory · Computer Science 2022-06-22 Gaojun Luo , Martianus Frederic Ezerman , San Ling

The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galois hulls of linear codes. Firstly, the symmetry of the…

Information Theory · Computer Science 2023-01-12 Yang Li , Shixin Zhu

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…

Information Theory · Computer Science 2014-03-12 Bocong Chen , San Ling , Guanghui Zhang

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…

Information Theory · Computer Science 2014-05-22 Liqi Wang , Shixin Zhu

We study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum…

Information Theory · Computer Science 2023-11-28 Philippe Gimenez , Diego Ruano , Rodrigo San-José

Absolutely maximally entangled (AME) states are pure multi-partite generalizations of the bipartite maximally entangled states with the property that all reduced states of at most half the system size are in the maximally mixed state. AME…

Quantum Physics · Physics 2018-02-14 Zahra Raissi , Christian Gogolin , Arnau Riera , Antonio Acín

Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…

Quantum Physics · Physics 2011-08-29 Mark M. Wilde

The intersection ${\bf C}\bigcap {\bf C}^{\perp_H}$ of a linear code ${\bf C} \subset {\bf F}_{q^2}$ and its Hermitian dual ${\bf C}^{\perp_H}$ is called the Hermitian hull of this code. A linear code ${\bf C} \subset {\bf F}_{q^2}$…

Information Theory · Computer Science 2022-09-27 Hao Chen

We construct quantum codes that support transversal $CCZ$ gates over qudits of arbitrary prime power dimension $q$ (including $q=2$) such that the code dimension and distance grow linearly in the block length. The only previously known…

Quantum Physics · Physics 2024-08-20 Louis Golowich , Venkatesan Guruswami

We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando , Ryutaroh Matsumoto

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…

Quantum Physics · Physics 2023-11-27 Markus Grassl , Thomas Beth , Martin Roetteler

We extend the relation between absolutely maximally entangled (AME) states and quantum maximum distance separable (QMDS) codes by constructing whole families of QMDS codes from their parent AME states. We introduce a reduction-friendly form…

Quantum Physics · Physics 2021-02-10 Daniel Alsina , Mohsen Razavi