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An inducing construction of quantum codes from classical error correcting codes

Published online by Cambridge University Press:  14 July 2016

K. R. Parthasarathy
K. R. Parthasarathy*
Affiliation:
Indian Statistical Institute
*
1Postal address: Indian Statistical Institute, Delhi Centre, 7 S. J. S. Sansanwal Marg, New Delhi 110 016, India. Email: [email protected]
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Abstract

The aim of the present paper is to construct error correcting quantum codes from classical error correcting group codes by using the Schur orthogonality relations for characters of a finite abelian group and the Knill–Laflamme criterion for a quantum code to correct a pre-assigned family of errors. This is an abstraction and generalization of Shor's example of a nine qubit single error correcting quantum code.

Keywords

Error correcting group codequantum codeWeyl commutation relationscharacters of an abelian group

MSC classification

Primary: 81P15: Quantum measurement theory
Type
Probability theory
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 27 - 32
Copyright
Copyright © Applied Probability Trust 2001 

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References

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