Abstract
Quantum jump codes (JC) are quantum codes which correct errors caused by quantum jumps. A spontaneous emission error design (SEED) has been introduced to construct quantum JC. In this paper the nonexistence of some \((n,m,t)_k\)-JCs is proved, where \(m={n-t\atopwithdelims ()k-t},\, k\ge t+1,\, \text{ and }\, (n,t,k)=(2k+1,1,k), (2k,2,k),(7,2,3),(8,3,4)\). It is also shown that, for these parameters with \(t=1,2\), the existence of an \((n,m,t)_k\)-JC is equivalent to that of a \(t-(n,k;m)\)-SEED.
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Acknowledgments
The authors would like to thank the anonymous referees for many valuable comments. Supported by NSFC Grants 11101026, 11271042, and the Fundamental Research Funds for the Central Universities 2011JBZ012
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Communicated by J.-L. Kim.
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Fang, J., Zhou, J. & Chang, Y. Nonexistence of some quantum jump codes with specified parameters. Des. Codes Cryptogr. 73, 223–235 (2014). https://doi.org/10.1007/s10623-013-9814-7
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DOI: https://doi.org/10.1007/s10623-013-9814-7