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In this paper, we theoretically study the relation between concurrence and nonlocality depicted by Bell-type inequality violation of quantum mechanics prediction versus local realism prediction for the GHZ (Greenberger -Horne-Zeilinger) class states. Analytical expressions of concurrence, violations of the Mermin inequality and the Svetlichny inequality are obtained. Through numerical calculations, the relationship between entanglement and nonlocality of GHZ-class states is discussed. Our results show that the concurrence is consistent with the degree of nonlocality described by violations of the two Bell-type inequalities of GHZ-class states. The Bell operator and its parameters can obviously reveal the nonlocal features of quantum states.
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Keywords:
- quantum information /
- GHZ-type states /
- concurrence /
- Bell-type inequalities
[1] Man Z X, Xia Y J 2007 Phys. Rev. A 75 052306
[2] Bennett C H, Brassard G, Crépeau C 1993 Phys. Rev. Lett. 70 1895
[3] Zheng Y Z, Gu Y J, Guo G C 2002 Chin. Phys. 11 537
[4] Prevedel T, Walther P, Tiefenbacher F 2007 Nature 445 05346
[5] Chen Z B, Pan J W, Zhang Y D 2003 Phys. Rev. Lett. 90 160408
[6] Xia Y J, Guo G C 2004 Chin. Phys. Lett. 21 1877
[7] Wang Z W, Zhou X F, Huang Y F, Zhang Y S, Ren X F, Guo G C 2006 Physics 35 913 (in Chinese) [王志伟, 周祥发, 黄运锋, 张永生, 任希锋, 郭光灿 2006 物理 35 913]
[8] Hossein N H, Stock R, James D F V 2009 Phys. Rev. A 80 022308
[9] Pan J W, Daniell M, Gasparoni S 2001 Phys. Rev. Lett. 86 4435
[10] Deutsch D, Ekert A, Jozsa R 1996 Phys. Rev. Lett. 77 2818
[11] Howell H C, Linares A L, Bouwmeester D 2002 Phys. Rev. Lett. 88 030401
[12] Ekert A1991 Phys. Rev. Lett. 67 611
[13] Mermin N D1990 Phys. Rev. Lett. 65 1838
[14] Bouwmeester D, Pan J W, Daniell M 1999 Phys. Rev. Lett. 82 1345
[15] Pan J W, Daniel M, Gasparoni S 2001 Phys. Rev. Lett. 86 4435
[16] Zhao Z, Yang T, Chen Y A 2003 Phys. Rev. Lett. 90 207901
[17] Ghose S, Sinclair N, Debnath S 2009 Phys. Rev. Lett. 102 250404
[18] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
[19] Miyake A 2003 Phys. Rev. A 67 012108
[20] Jungnitsch B, Niekamp S, Kleinmann M 2010 Phys. Rev. Lett. 104 210401
[21] Lu H X, Zhao J Q, Wang X Q 2011 Phys. Rev. A 84 044101
[22] Zhao J Q, Cao L Z, Wang X Q, Lu H X 2012 Phys. Lett. A 376 2377
[23] Zhao J Q, Cao L Z, Wang X Q, Lu H X 2012 Acta Phys. Sin. 61 170301 (in Chinese) [赵加强, 曹连振, 王晓芹, 逯怀新 2012 61 170301]
[24] Svetlichny G 1987 Phys. Rev. D 35 3066
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[1] Man Z X, Xia Y J 2007 Phys. Rev. A 75 052306
[2] Bennett C H, Brassard G, Crépeau C 1993 Phys. Rev. Lett. 70 1895
[3] Zheng Y Z, Gu Y J, Guo G C 2002 Chin. Phys. 11 537
[4] Prevedel T, Walther P, Tiefenbacher F 2007 Nature 445 05346
[5] Chen Z B, Pan J W, Zhang Y D 2003 Phys. Rev. Lett. 90 160408
[6] Xia Y J, Guo G C 2004 Chin. Phys. Lett. 21 1877
[7] Wang Z W, Zhou X F, Huang Y F, Zhang Y S, Ren X F, Guo G C 2006 Physics 35 913 (in Chinese) [王志伟, 周祥发, 黄运锋, 张永生, 任希锋, 郭光灿 2006 物理 35 913]
[8] Hossein N H, Stock R, James D F V 2009 Phys. Rev. A 80 022308
[9] Pan J W, Daniell M, Gasparoni S 2001 Phys. Rev. Lett. 86 4435
[10] Deutsch D, Ekert A, Jozsa R 1996 Phys. Rev. Lett. 77 2818
[11] Howell H C, Linares A L, Bouwmeester D 2002 Phys. Rev. Lett. 88 030401
[12] Ekert A1991 Phys. Rev. Lett. 67 611
[13] Mermin N D1990 Phys. Rev. Lett. 65 1838
[14] Bouwmeester D, Pan J W, Daniell M 1999 Phys. Rev. Lett. 82 1345
[15] Pan J W, Daniel M, Gasparoni S 2001 Phys. Rev. Lett. 86 4435
[16] Zhao Z, Yang T, Chen Y A 2003 Phys. Rev. Lett. 90 207901
[17] Ghose S, Sinclair N, Debnath S 2009 Phys. Rev. Lett. 102 250404
[18] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
[19] Miyake A 2003 Phys. Rev. A 67 012108
[20] Jungnitsch B, Niekamp S, Kleinmann M 2010 Phys. Rev. Lett. 104 210401
[21] Lu H X, Zhao J Q, Wang X Q 2011 Phys. Rev. A 84 044101
[22] Zhao J Q, Cao L Z, Wang X Q, Lu H X 2012 Phys. Lett. A 376 2377
[23] Zhao J Q, Cao L Z, Wang X Q, Lu H X 2012 Acta Phys. Sin. 61 170301 (in Chinese) [赵加强, 曹连振, 王晓芹, 逯怀新 2012 61 170301]
[24] Svetlichny G 1987 Phys. Rev. D 35 3066
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