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We find a new approach to study nice error bases and quantum error-correcting codes, namely the group algebra which gives us an algebraic notation for nice error bases and quantum codes. From this algebraic notation we establish a series of linear programming bounds on the most general quantum error-correcting codes.
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Keywords:
- group algebra /
- error bases /
- 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, Xing L J 2007 Acta Phys. Sin. 56 5602 (in Chinese) [李卓, 邢莉娟 2007 56 5602]
[3] Xing L J, Li Z, Bai B M, Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese) [邢莉娟, 李卓, 白宝明, 王新梅 2008 57 4695]
[4] Li Z, Xing L J, Wang X M 2009 IEEE Trans. Inform. Theory 55 3821
[5] Li Z, Xing L J, Wang X M 2008 Phys. Rev. A77 012308
[6] Li Z, Xing L J 2009 Phys. Rev. A79 032301
[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] Steane A M 1996 Phys. Rev. Lett. 77 793
[10] Knill E 1996 Los Alamos Nat. Lab. Rep. LAUR-96-2717
[11] Ashikhmin A, Knill E 2001 IEEE Trans. Inform. Theory 47 3065
[12] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1998 IEEE Trans. Inform. Theory 44 1369
[13] Rains E M 1999 IEEE Trans. Inform. Theory 45 2361
[14] Ketkar A, Klappenecker A, Kumar S, Sarvepalli P K 2006 IEEE Trans. Inform. Theory 52 4892
[15] Klappenecker A, Rotteler M 2002 IEEE Trans. Inform. Theory 48 2392
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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, Xing L J 2007 Acta Phys. Sin. 56 5602 (in Chinese) [李卓, 邢莉娟 2007 56 5602]
[3] Xing L J, Li Z, Bai B M, Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese) [邢莉娟, 李卓, 白宝明, 王新梅 2008 57 4695]
[4] Li Z, Xing L J, Wang X M 2009 IEEE Trans. Inform. Theory 55 3821
[5] Li Z, Xing L J, Wang X M 2008 Phys. Rev. A77 012308
[6] Li Z, Xing L J 2009 Phys. Rev. A79 032301
[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] Steane A M 1996 Phys. Rev. Lett. 77 793
[10] Knill E 1996 Los Alamos Nat. Lab. Rep. LAUR-96-2717
[11] Ashikhmin A, Knill E 2001 IEEE Trans. Inform. Theory 47 3065
[12] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1998 IEEE Trans. Inform. Theory 44 1369
[13] Rains E M 1999 IEEE Trans. Inform. Theory 45 2361
[14] Ketkar A, Klappenecker A, Kumar S, Sarvepalli P K 2006 IEEE Trans. Inform. Theory 52 4892
[15] Klappenecker A, Rotteler M 2002 IEEE Trans. Inform. Theory 48 2392
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