Quantum generalized Reed-Solomon codes: Unified framework for quantum maximum-distance-separable codes

被引：200

作者：

Li, Zhuo ^{[1
]}

Xing, Li-Juan ^{[1
]}

Wang, Xin-Mei ^{[1
]}

机构：

[1] Xidian Univ, State Key Lab Integrated Serv Networks, Xian 710071, Shaanxi, Peoples R China

来源：

PHYSICAL REVIEW A | 2008年 / 77卷 / 01期

关键词：

D O I：

10.1103/PhysRevA.77.012308

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We construct a family of quantum maximum-distance-separable (MDS) codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus, as far as is known at present, they are the most important family of quantum MDS codes.

引用

页数：4

共 16 条

[1] Nonbinary quantum stabilizer codes [J].

Ashikhmin, A ;

Knill, E .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (07) :3065-3072

[2]

Bennett CH, 1996, PHYS REV A, V54, P3824, DOI 10.1103/PhysRevA.54.3824

[3] Good quantum error-correcting codes exist [J].

Calderbank, AR ;

Shor, PW .

PHYSICAL REVIEW A, 1996, 54 (02) :1098-1105

[4] Quantum-error correction and orthogonal geometry [J].

Calderbank, AR ;

Rains, EM ;

Shor, PW ;

Sloane, NJA .

PHYSICAL REVIEW LETTERS, 1997, 78 (03) :405-408

[5] Five quantum register error correction code for higher spin systems [J].

Chau, HF .

PHYSICAL REVIEW A, 1997, 56 (01) :R1-R4

[6] Quantum codes [[6,2,3]]p and [[7,3,3]]p (p ≥ 3) exist [J].

Feng, KQ .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (08) :2384-2391

[7] Class of quantum error-correcting codes saturating the quantum Hamming hound [J].

Gottesman, D .

PHYSICAL REVIEW A, 1996, 54 (03) :1862-1868

[8] On optimal quantum codes [J].

Grassl, M ;

Beth, T ;

Rötteler, M .

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2004, 2 (01) :55-64

[9] Theory of quantum error-correcting codes [J].

Knill, E ;

Laflamme, R .

PHYSICAL REVIEW A, 1997, 55 (02) :900-911

[10] Perfect quantum error correcting code [J].

Laflamme, R ;

Miquel, C ;

Paz, JP ;

Zurek, WH .

PHYSICAL REVIEW LETTERS, 1996, 77 (01) :198-201

← 1 2 →