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By studying sets of operators with constant weight we present for the first time an analytical upper bound on the pure quantum stabilizer codes whose underlying quantum system can be of arbitrary dimension, which outperforms the so far well-known quantum Hamming bound, the optimal analytical upper bound for small code length.
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Keywords:
- quantum Hamming bound /
- quantum stabilizer codes /
- quantum error-correcting codes /
- quantum information
[1] Li Z, Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese) [李 卓、邢莉娟 2008 57 28]
[2] Li Z and Xing L J 2007 Acta Phys. Sin. 56 5602 (in Chinese) [李 卓、邢莉娟 2007 565602]
[3] Xing L J, Li Z, Bai B M, Wang X M 2008 Acta Phys. Sin. 574695 (in Chinese) [邢莉娟、李 卓、白宝明、王新梅 2008 物 理学报 574695] [4] Li Z, Xing L J, Wang X M 2009 IEEE Trans. Inform. Theory 55 3821
[4] Li Z, Xing L J, Wang X M 2008 Phys. Rev. A77 012308
[5] Laflamme R, Miquel C, Paz J P, Zurek W 1996 Phys. Rev. Lett. 77 198
[6] Steane A M 1996 Phys. Rev. Lett. 77 793
[7] Shor P W 1995 Phys. Rev. A52 2493
[8] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1997 Phys. Rev. Lett. 78 405
[9] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1998 IEEE Trans. Inform. Theory 44 1369
[10] Ketkar A, Klappenecker A, Kumar S, Sarvepalli P K 2006 IEEE Trans. Inform. Theory 52 4892
[11] Ashikhmin A, Knill E 2001 IEEE Trans. Inform. Theory 47 3065
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[1] Li Z, Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese) [李 卓、邢莉娟 2008 57 28]
[2] Li Z and Xing L J 2007 Acta Phys. Sin. 56 5602 (in Chinese) [李 卓、邢莉娟 2007 565602]
[3] Xing L J, Li Z, Bai B M, Wang X M 2008 Acta Phys. Sin. 574695 (in Chinese) [邢莉娟、李 卓、白宝明、王新梅 2008 物 理学报 574695] [4] Li Z, Xing L J, Wang X M 2009 IEEE Trans. Inform. Theory 55 3821
[4] Li Z, Xing L J, Wang X M 2008 Phys. Rev. A77 012308
[5] Laflamme R, Miquel C, Paz J P, Zurek W 1996 Phys. Rev. Lett. 77 198
[6] Steane A M 1996 Phys. Rev. Lett. 77 793
[7] Shor P W 1995 Phys. Rev. A52 2493
[8] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1997 Phys. Rev. Lett. 78 405
[9] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1998 IEEE Trans. Inform. Theory 44 1369
[10] Ketkar A, Klappenecker A, Kumar S, Sarvepalli P K 2006 IEEE Trans. Inform. Theory 52 4892
[11] Ashikhmin A, Knill E 2001 IEEE Trans. Inform. Theory 47 3065
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