Error Correcting Codes in Quantum Theory.

@article{Steane1996ErrorCC,
  title={Error Correcting Codes in Quantum Theory.},
  author={Steane},
  journal={Physical review letters},
  year={1996},
  volume={77 5},
  pages={
          793-797
        }
}
  • Steane
  • Published 1996
  • Physics, Medicine
  • Physical review letters
A new type of uncertainty relation is presented, concerning the information-bearing properties of a discrete quantum system. A natural link is then revealed between basic quantum theory and the linear error correcting codes of classical information theory. A subset of the known codes is described, having properties which are important for error correction in quantum communication. It is shown that a pair of states which are, in a certain sense, “macroscopically different,” can form a… Expand

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References

SHOWING 1-10 OF 11 REFERENCES
The Theory of Error-Correcting Codes
Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the Golay Code. An Introduction to BCH Codes and Finite Fields. Finite Fields. Dual Codes and Their Weight Distribution. Codes, DesignsExpand
Bell Syst
  • Tech. J 29, 147
  • 1950
Naturwissenschaften 23
  • 807 (1935); translated inQuantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek
  • 1983
Phys
  • Rev. Lett. 50, 631
  • 1983
Phys
  • Rev. A52, R2493
  • 1995
Quantum Theory: Concepts and Method
  • (Kluwer Academic,
  • 1993
Phys
  • Rev. Lett. 65, 1838
  • 1990
Phys
  • Rev. Lett. 60, 1103
  • 1988
Proc
  • R. Soc. London A 400, 97
  • 1985
...
1
2
...