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In this paper, we produce some new classes of entanglement-assisted quantum MDS codes(EAQMDS codes for short) via generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many EAQMDS codes…

Information Theory · Computer Science 2020-08-27 Renjie Jin , Yiran Cao , Jinquan Luo

A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented. Relations of symplectic subspaces and quaternary additive codes concerning parameters of EAQECCs…

Quantum Physics · Physics 2025-08-13 Ruihu Li , Yuezhen Ren , Chaofeng Guan , Yang Liu

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…

Quantum Physics · Physics 2007-05-23 Todd Brun , Igor Devetak , Min-Hsiu Hsieh

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

Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new…

Information Theory · Computer Science 2019-01-11 Mehmet E. Koroglu

Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…

Quantum Physics · Physics 2015-05-30 Jeonghwan Shin , Jun Heo , Todd A. Brun

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

Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…

Quantum Physics · Physics 2013-04-24 Yuichiro Fujiwara

Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional…

Information Theory · Computer Science 2019-11-18 Francisco Revson F. Pereira

The hull of linear codes plays an important role in quantum information and coding theory. In the present paper, by investigating the Galois hulls of generalized Reed-Solomon (GRS) codes and extended GRS codes over the finite field Fq, we…

Information Theory · Computer Science 2020-04-07 Meng Cao

Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a…

Information Theory · Computer Science 2021-08-03 Xiaolei Fang , Renjie Jin , Jinquan Luo , Wen Ma

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

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

We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…

Quantum Physics · Physics 2026-03-04 Jaszmine DeFranco , Andrew Nemec

Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…

We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,\cdots, W_S$ over a finite field $\mathbb{F}_d$. A user aims…

Information Theory · Computer Science 2025-01-28 Lei Hu , Mohamed Nomeir , Alptug Aytekin , Yu Shi , Sennur Ulukus , Saikat Guha

We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…

Quantum Physics · Physics 2007-11-13 Mark M. Wilde , Hari Krovi , Todd A. Brun

We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block…

Quantum Physics · Physics 2009-02-11 Mark M. Wilde , Todd A. Brun

We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…

Quantum Physics · Physics 2010-02-20 Isaac Kremsky , Min-Hsiu Hsieh , Todd A. Brun

An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to…

Quantum Physics · Physics 2014-01-28 Mark M. Wilde , Min-Hsiu Hsieh , Zunaira Babar