Effect of excess noise on continuous variable entanglement sudden death and Gaussian quantum discord

doi:10.1088/1674-1056/22/8/080304

Abstract A symmetric two-mode Gaussian entangled state is used to investigate the effect of excess noise on entanglement sudden death and Gaussian quantum discord with continuous variables. The results show that the excess noise in the channel can lead to entanglement sudden death of a symmetric two-mode Gaussian entangled state, while Gaussian quantum discord never vanishes. As a practical application, the security of a quantum key distribution (QKD) scheme based on a symmetric two-mode Gaussian entangled state against collective Gaussian attacks is analyzed. The calculation results show that the secret key cannot be distilled when entanglement vanishes and only quantum discord exists in such a QKD scheme.

Keywords: continuous variable entanglement quantum key distribution

Received: 10 January 2013
Revised: 06 March 2013
Accepted manuscript online:

PACS:	03.67.Hk	(Quantum communication)
	03.67.Dd	(Quantum cryptography and communication security)
	42.50.Dv	(Quantum state engineering and measurements)
	42.50.-p	(Quantum optics)

Fund: Project supported by the National Basic Research Program of China (Grant No. 2010CB923103), the National Natural Science Foundation of China (Grant Nos. 11174188 and 61121064), and the Fund from the Shanxi Scholarship Council of China (Grant No. 2012-010).

Corresponding Authors: Su Xiao-Long
E-mail: suxl@sxu.edu.cn

Cite this article:

Su Xiao-Long (苏晓龙) Effect of excess noise on continuous variable entanglement sudden death and Gaussian quantum discord 2013 Chin. Phys. B 22 080304

[1]	Yu T and Eberly J H 2009 Science 323 598
[2]	Almeida M P, De Melo F, Hor-Meyll M, Salles A, Walborn S P, Souto Ribeiro P H and Davidovich L 2007 Science 316 579
[3]	Braunstein S L and Van Loock P 2005 Rev. Mod. Phys. 77 513
[4]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H and Llyod S 2012 Rev. Mod. Phys. 84 621
[5]	Coelho A S, Barbosa F A S, Cassemiro K N, Villar A S, Martinelli M, and Nussemzveig P 2009 Science 326 823
[6]	Barbosa F A S, Coelho A S, De Faria A J, Cassemiro K N, Villar A S, Nussemzveig P and Martinelli M 2010 Nat. Photon. 4 858
[7]	Barbosa F A S, De Faria A J, Coelho A S, Cassemiro K N, Villar A S, Nussemzveig P and Martinelli M 2011 Phys. Rev. A 84 052330
[8]	Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
[9]	Knill E and Laflamme R 1998 Phys. Rev. Lett. 81 5672
[10]	Ryan C A, Emerson J, Poulin D, Negrevergne C and Laflamme R 2005 Phys. Rev. Lett. 95 250502
[11]	Lanyon B P, Barbieri M, Almeida M P and White A G 2008 Phys. Rev. Lett. 101 200501
[12]	Giorda P and Paris M G A 2010 Phys. Rev. Lett. 105 020503
[13]	Adesso G and Datta A 2010 Phys. Rev. Lett. 105 030501
[14]	Gu M, Chrzanowski H M, Assad S M, Symul T, Modi K, Ralph T C, Vedral V and Lam P K 2012 Nat. Phys. 8 671
[15]	Blandino R, Genoni M G, Etesse J, Barbieri M, Paris M G A, Grangier P and Tualle-Brouri Rosa 2012 Phys. Rev. Lett. 109 180402
[16]	Madsen L S, Berni A, Lassen M and Andersen U L 2012 Phys. Rev. Lett. 109 030402
[17]	Chen J J, Han Z F, Zhao Y B, Gui Y Z and Guo G C 2006 Physics 35 785 (in Chinese)
[18]	Zhu J, He G Q and Zeng G H 2007 Chin. Phys. 16 1364
[19]	Namiki R and Hirano T 2004 Phys. Rev. Lett. 92 117901
[20]	Renner R and Cirac J I 2009 Phys. Rev. Lett. 102 110504
[21]	Leverrier A and Grangier P 2009 Phys. Rev. Lett. 102 180504
[22]	Su X L, Jing J T, Pan Q and Xie C D 2006 Phys. Rev. A 74 062305
[23]	Pirandola S, Mancini S, Lloyd S and Braunstein S L 2008 Nat. Phys. 4 726
[24]	Weedbrook C, Pirandola S and Ralph T C 2012 Phys. Rev. A 86 022318
[25]	Grosshans F, Van Assche G, Wenger J, Brouri R, Cerf N J and Grangier P 2003 Nature 421 238
[26]	Lorenz S, Korolkova N and Leuchs G 2004 Appl. Phys. B 79 273
[27]	Lance A M, Symul T, Sharma V, Weedbrook C, Ralph T C and Lam P K 2005 Phys. Rev. Lett. 95 180503
[28]	Symul T, Alton D J, Assad S M, Lance A M, Weedbrook C, Ralph T C and Lam P K 2007 Phys. Rev. A 76 030303
[29]	Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R, McLaughlin S W and Grangier P 2007 Phys. Rev. A 76 042305
[30]	Qi B, Huang L L, Qian L and Lo H K 2007 Phys. Rev. A 76 052323
[31]	Shen Y, Zou H X, Tian L, Chen P X and Yuan J M 2010 Phys. Rev. A 82 022317
[32]	Su X L, Wang W Z, Wang Y, Jia X J, Xie C D and Peng K C 2009 Europhys. Lett. 87 20005
[33]	Eberle Tobias, Händchen Vitus, Duhme J, Franz T, Werner R F and Schnabel R arXiv: 1110.3977v1 [quant-ph]
[34]	Madsen L S, Usenko V C, Lassen M, Filip R and Andersen U L 2012 Nature Commun. 3 1083
[35]	Curty M, Lewenstein M and Lütkenhaus N 2004 Phys. Rev. Lett. 92 217903
[36]	Serafini A, Illuminati F and De Siena S 2004 J. Phys. B: At. Mol. Opt. Phys. 37 L21
[37]	Adesso G, Serafini A and Illuminati F 2004 Phys. Rev. A 70 022318
[38]	Simon R 2000 Phys. Rev. Lett. 84 2726
[39]	Werner R F and Wolf M M 2001 Phys. Rev. Lett. 86 3658
[40]	Silberhorn Ch, Ralph T C, Lütkenhaus N and Leuchs G 2002 Phys. Rev. Lett. 89 167901
[41]	Grosshans F, Cerf N J, Wenger J, Tualle-Brouri R and Grangier P 2003 Quantum Inf. Comput. 3 535
[42]	Navascués M, Grosshans G and Acín A 2006 Phys. Rev. Lett. 97 190502
[43]	García-Patrón R and Cerf N J 2006 Phys. Rev. Lett. 97 190503
[44]	Pirandola S, Braunstein S L and Lloyd S 2008 Phys. Rev. Lett. 101 200504
[45]	Grosshans F and Grangier P 2002 Phys. Rev. Lett. 88 057902
[46]	Holevo A S, Sohma M and Hirota O 1999 Phys. Rev. A 59 1820
[47]	Grangier P, Levenson J A and Poizat J P 1998 Nature 396 537
[48]	Eisert J, Scheel S and Plenio M B 2002 Phys. Rev. Lett. 89 137903
[49]	Fiurášek J 2002 Phys. Rev. Lett. 89 137904

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Effect of excess noise on continuous variable entanglement sudden death and Gaussian quantum discord

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