Affordable Access

Quantum shadow enumerators

Authors
  • Rains, E. M.
Type
Published Article
Publication Date
Feb 19, 1997
Submission Date
Nov 01, 1996
Identifiers
arXiv ID: quant-ph/9611001
Source
arXiv
License
Unknown
External links

Abstract

In a recent paper [quant-ph/9610040], Shor and Laflamme define two ``weight enumerators'' for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We extend their work by introducing another enumerator, based on the classical theory of shadow codes, that tightens their bounds significantly. In particular, nearly all of the codes known to be optimal among additive quantum codes (codes derived from orthogonal geometry ([quant-ph/9608006])) can be shown to be optimal among all quantum codes. We also use the shadow machinery to extend a bound on additive codes (E. M. Rains, manuscript in preparation) to general codes, obtaining as a consequence that any code of length n can correct at most floor((n+1)/6) errors.

Report this publication

Statistics

Seen <100 times