Upper bounds on the size of quantum codes

Alexei Ashikhmin; Simon Litsyn

doi:10.1109/18.761270

Upper bounds on the size of quantum codes

Alexei Ashikhmin, Simon Litsyn

Los Alamos National Laboratory

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates.

Original language	English
Pages (from-to)	1206-1215
Number of pages	10
Journal	IEEE Transactions on Information Theory
Volume	45
Issue number	4
DOIs	https://doi.org/10.1109/18.761270
State	Published - 1999
Externally published	Yes

Access to Document

10.1109/18.761270

Cite this

@article{2dfa7c6b858141f0bf13936f447e7ffe,

title = "Upper bounds on the size of quantum codes",

abstract = "This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates.",

author = "Alexei Ashikhmin and Simon Litsyn",

year = "1999",

doi = "10.1109/18.761270",

language = "אנגלית",

volume = "45",

pages = "1206--1215",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}

TY - JOUR

T1 - Upper bounds on the size of quantum codes

AU - Ashikhmin, Alexei

AU - Litsyn, Simon

PY - 1999

Y1 - 1999

N2 - This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates.

AB - This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates.

UR - http://www.scopus.com/inward/record.url?scp=0032656276&partnerID=8YFLogxK

U2 - 10.1109/18.761270

DO - 10.1109/18.761270

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0032656276

SN - 0018-9448

VL - 45

SP - 1206

EP - 1215

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

ER -

Upper bounds on the size of quantum codes

Abstract

Access to Document

Other files and links

Fingerprint

Cite this