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Boolean functions, projection operators, and quantum error correcting codes

Publication ,  Journal Article
Aggarwal, V; Calderbank, AR
Published in: IEEE Transactions on Information Theory
April 1, 2008

This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5, 6, 2)) code found by Rains et al It also extends to operator quantum error correcting codes. © 2008 IEEE.

Duke Scholars

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

April 1, 2008

Volume

54

Issue

4

Start / End Page

1700 / 1707

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Aggarwal, V., & Calderbank, A. R. (2008). Boolean functions, projection operators, and quantum error correcting codes. IEEE Transactions on Information Theory, 54(4), 1700–1707. https://doi.org/10.1109/TIT.2008.917720
Aggarwal, V., and A. R. Calderbank. “Boolean functions, projection operators, and quantum error correcting codes.” IEEE Transactions on Information Theory 54, no. 4 (April 1, 2008): 1700–1707. https://doi.org/10.1109/TIT.2008.917720.
Aggarwal V, Calderbank AR. Boolean functions, projection operators, and quantum error correcting codes. IEEE Transactions on Information Theory. 2008 Apr 1;54(4):1700–7.
Aggarwal, V., and A. R. Calderbank. “Boolean functions, projection operators, and quantum error correcting codes.” IEEE Transactions on Information Theory, vol. 54, no. 4, Apr. 2008, pp. 1700–07. Scopus, doi:10.1109/TIT.2008.917720.
Aggarwal V, Calderbank AR. Boolean functions, projection operators, and quantum error correcting codes. IEEE Transactions on Information Theory. 2008 Apr 1;54(4):1700–1707.

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

April 1, 2008

Volume

54

Issue

4

Start / End Page

1700 / 1707

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing