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By solving the Milburn equation, we investigate the properties of optimal channel capacity for the quantum dense coding via a two-qubit Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence. The influences of different DM interactions, different initial states, anisotropic coupling parameters, and intrinsic decoherence on optimal coding capacity are analyzed in detail. It is found that the initial state of the system affects optimal coding capacity greatly, whose dependent parameters are not identical for different types of initial states. When the system is initially in the form of the nonmaximally entangled state cft| {01} ightangle + dft| {10} ightangle , a weak z-component DM interaction can enhance the value of optimal coding capacity as compared with the value without DM interaction, and the phase decoherence effect can suppress the oscillation of optimal coding capacity and make the capacity decrease to a stable value for the long-time evolution. It is also found that under the influence of intrinsic decoherence, the optimal transmission capacity of dense coding can keep an ideal maximal value of 2 by choosing the proper initial maximally entangled state. Moreover, no matter from which direction the DM interaction is introduced, the optimal coding capacity via the two-qubit Heisenberg spin system is always larger than the transmission capacity of any classical communication.
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Keywords:
- Heisenberg model /
- Dzyaloshinski-Moriya interaction /
- intrinsic decoherence /
- optimal coding capacity
[1] Ekert A K 1991 Phys. Rev. Lett. 67 661
[2] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[3] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[4] Barenco A, Ekert A K 1995 J. Mod. Opt. 42 1253
[5] Hao J C, Li C F, Guo G C 2001 Phys. Rev. A 63 054301
[6] Zhang J, Xie C D, Peng K C 2002 Phys. Rev. A 66 032318
[7] Liu X S, Long G L, Tong D M, Li F 2002 Phys. Rev. A 65 022304
[8] Li L Z, Qiu D W 2007 J. Phys. A: Math. Theor. 40 10871
[9] Wang M Y, Yan F L 2011 Chin. Phys. B 20 120309
[10] Horodecki M, Piani M 2012 J. Phys. A: Math. Theor. 45 105306
[11] Yang Y G, Xia J, Jia X, Zhang H 2012 Int. J. Theor. Phys. 51 1917
[12] Quek S, Li Z, Yeo Y 2010 Phys. Rev. A 81 024302
[13] Shadman Z, Kampermann H, Macchiavello C, Bruss D 2010 New J. Phys. 12 073042
[14] Metwally N 2011 J. Phys. A: Math. Theor. 44 055305
[15] Mattle K, Weinfurter H, Kwait P G, Zeilinger A 1996 Phys. Rev. Lett. 76 4656
[16] Li X, Pan Q, Jing J, Zhang J, Xie C, Peng K 2002 Phys. Rev. Lett. 88 047904
[17] Barreiro J T, Wei T C, Kwiat P G 2008 Nat. Phys. 4 282
[18] Fang X, Zhu X, Feng M, Mao X, Du F 2000 Phys. Rev. A 61 022307
[19] Wang X G 2001 Phys. Rev. A 64 012313
[20] Kamta G L, Starace A F 2002 Phys. Rev. Lett. 88 107901
[21] Wang H, Wu G X 2013 Chin. Phys. B 22 050512
[22] Ji A C, Xie X C, Liu W M 2007 Phys. Rev. Lett. 99 183602
[23] Yu P F, Cai J G, Liu J M, Shen G T 2007 Eur. Phys. J. D 44 151
[24] Li D C, Cao Z L 2008 Eur. Phys. J. D 50 207
[25] Xu X B, Liu J M, Yu P F 2008 Chin. Phys. B 17 0456
[26] Zhang G F 2008 Phys. Scr. 79 015001
[27] Jiang C L, Liu X J, Liu M W, Wang Y H, Peng C H 2012 Acta Phys. Sin. 61 170302 (in Chinese) [姜春蕾, 刘晓娟, 刘明伟, 王艳辉, 彭朝晖 2012 物理学报 61 170302]
[28] Qin M, Li Y B, Bai Z, Wang X 2014 Acta Phys. Sin. 63 110302 (in Chinese) [秦猛, 李延标, 白忠, 王晓 2014 物理学报 63 110302]
[29] Abliz A, Gao H J, Xie X C, Wu Y S, Liu W M 2006 Phys. Rev. A 74 052105
[30] Qiu L, Wang A M, Su X Q, Ma X S 2009 Phys. Scr. 79 015005
[31] Cai J T, Abliz A, Bai Y K, Jin G S 2011 Chin. Phys. Lett. 28 020307
[32] Huang H L, Sun Z Y 2014 Appl. Mech. Mater. 446-447 986
[33] Dzyaloshinskii I 1958 J. Phys. Chem. Solid 4 241
[34] Moriya T 1960 Phys. Rev. Lett. 4 228
[35] Carmichael H J 1993 An Open Systems Approach to Quantum Optics (Berlin: Springer Verlag)
[36] Li Z G, Fei S M, Wang Z D, Liu W M 2009 Phys. Rev. A 79 024303
[37] Milburn G J 1991 Phys. Rev. A 44 5401
[38] Xu J B, Zou X B, Yu J H 2000 Eur. Phys. J. D 10 295
[39] Hiroshima T 2001 J. Phys. A: Math. Gen. 34 6907
[40] Qiu L, Wang A M, Ma X S 2007 Physica A 383 325
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[1] Ekert A K 1991 Phys. Rev. Lett. 67 661
[2] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[3] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[4] Barenco A, Ekert A K 1995 J. Mod. Opt. 42 1253
[5] Hao J C, Li C F, Guo G C 2001 Phys. Rev. A 63 054301
[6] Zhang J, Xie C D, Peng K C 2002 Phys. Rev. A 66 032318
[7] Liu X S, Long G L, Tong D M, Li F 2002 Phys. Rev. A 65 022304
[8] Li L Z, Qiu D W 2007 J. Phys. A: Math. Theor. 40 10871
[9] Wang M Y, Yan F L 2011 Chin. Phys. B 20 120309
[10] Horodecki M, Piani M 2012 J. Phys. A: Math. Theor. 45 105306
[11] Yang Y G, Xia J, Jia X, Zhang H 2012 Int. J. Theor. Phys. 51 1917
[12] Quek S, Li Z, Yeo Y 2010 Phys. Rev. A 81 024302
[13] Shadman Z, Kampermann H, Macchiavello C, Bruss D 2010 New J. Phys. 12 073042
[14] Metwally N 2011 J. Phys. A: Math. Theor. 44 055305
[15] Mattle K, Weinfurter H, Kwait P G, Zeilinger A 1996 Phys. Rev. Lett. 76 4656
[16] Li X, Pan Q, Jing J, Zhang J, Xie C, Peng K 2002 Phys. Rev. Lett. 88 047904
[17] Barreiro J T, Wei T C, Kwiat P G 2008 Nat. Phys. 4 282
[18] Fang X, Zhu X, Feng M, Mao X, Du F 2000 Phys. Rev. A 61 022307
[19] Wang X G 2001 Phys. Rev. A 64 012313
[20] Kamta G L, Starace A F 2002 Phys. Rev. Lett. 88 107901
[21] Wang H, Wu G X 2013 Chin. Phys. B 22 050512
[22] Ji A C, Xie X C, Liu W M 2007 Phys. Rev. Lett. 99 183602
[23] Yu P F, Cai J G, Liu J M, Shen G T 2007 Eur. Phys. J. D 44 151
[24] Li D C, Cao Z L 2008 Eur. Phys. J. D 50 207
[25] Xu X B, Liu J M, Yu P F 2008 Chin. Phys. B 17 0456
[26] Zhang G F 2008 Phys. Scr. 79 015001
[27] Jiang C L, Liu X J, Liu M W, Wang Y H, Peng C H 2012 Acta Phys. Sin. 61 170302 (in Chinese) [姜春蕾, 刘晓娟, 刘明伟, 王艳辉, 彭朝晖 2012 物理学报 61 170302]
[28] Qin M, Li Y B, Bai Z, Wang X 2014 Acta Phys. Sin. 63 110302 (in Chinese) [秦猛, 李延标, 白忠, 王晓 2014 物理学报 63 110302]
[29] Abliz A, Gao H J, Xie X C, Wu Y S, Liu W M 2006 Phys. Rev. A 74 052105
[30] Qiu L, Wang A M, Su X Q, Ma X S 2009 Phys. Scr. 79 015005
[31] Cai J T, Abliz A, Bai Y K, Jin G S 2011 Chin. Phys. Lett. 28 020307
[32] Huang H L, Sun Z Y 2014 Appl. Mech. Mater. 446-447 986
[33] Dzyaloshinskii I 1958 J. Phys. Chem. Solid 4 241
[34] Moriya T 1960 Phys. Rev. Lett. 4 228
[35] Carmichael H J 1993 An Open Systems Approach to Quantum Optics (Berlin: Springer Verlag)
[36] Li Z G, Fei S M, Wang Z D, Liu W M 2009 Phys. Rev. A 79 024303
[37] Milburn G J 1991 Phys. Rev. A 44 5401
[38] Xu J B, Zou X B, Yu J H 2000 Eur. Phys. J. D 10 295
[39] Hiroshima T 2001 J. Phys. A: Math. Gen. 34 6907
[40] Qiu L, Wang A M, Ma X S 2007 Physica A 383 325
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