Krawtchouk多项式与纯的加性量子纠错码的上界
doi: 10.3724/SP.J.1146.2006.00304
Krawtchouk Polynomials and Upper Bounds for Pure Additive Quantum Error Correcting Codes
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摘要: 该文利用Krawtchouk多项式函数给出了纯的加性量子纠错码的两个不同的上界，并进一步证明了量子Singleton界和渐近量子Hamming界只是这两个上界的特例。Abstract: Two universal bounds for pure additive quantum error correcting codes are obtained by using of Krawtchouk polynomials, and it is proved that the quantum Singleton bound and the asymptotic quantum Hamming bound are just the special cases of those two universal bounds.
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Bennett C H, Divincenzo G, and Smolin J A, et al.. Mixed state entanglement and quantum error correction[J].Phys. Rev. A.1996, 54:3824-3851[2]Knill E and Laflamme R. A theory of quantum error-correcting codes[J].Phys. Rev. A.1997, 55:900-911[3]Calderbank A R, Shor E M, and Shor P W, et al.. Quantum error correction via codes over GF(4)[J].IEEE Trans. on Inform. Theory.1998, 44(4):1369-1387[4]Levershtein V I. Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces[J].IEEE Trans. on Inform. Theory.1995, 41(5):1303-1320 -
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