Comparative analysis of entanglement measures based on monogamy inequality

doi:10.1088/1674-1056/26/5/050301

Abstract We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation (EOF) tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors (containing GHZ and superposition of W-, obverse W states) either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.

Keywords: monogamy of quantum entanglement concurrence tangle negativity tangle Majorana representation of symmetric pure states

Received: 24 November 2016
Revised: 01 February 2017
Accepted manuscript online:

PACS:	03.65.Ud	(Entanglement and quantum nonlocality)
	03.67.Bg	(Entanglement production and manipulation)

Corresponding Authors: Sudha
E-mail: arss@rediffmail.com

Cite this article:

P J Geetha, Sudha, K S Mallesh Comparative analysis of entanglement measures based on monogamy inequality 2017 Chin. Phys. B 26 050301

[1]	Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[2]	Koashi M, Buzek V and Imoto N 2000 Phys. Rev. A 62 050302(R)
[3]	Dennison K A and Wootters W K 2001 Phys. Rev. A 65 010301(R)
[4]	Terhal B M 2004 IBM Journal of Research and Development 48 71(quant-ph/arxiv 0307120)
[5]	Koashi M and Winter A 2004 Phys. Rev. A 69 022309
[6]	Gour G, Meyer D A and Sanders B C 2005 Phys. Rev. A 72 042329
[7]	Osborne T J and Verstraete F 2006 Phys. Rev. Lett. 96 220503
[8]	D Yang 2006 Phys. Lett. A 360 249
[9]	Y C Ou 2007 Phys. Rev. A 75 034305
[10]	Y C Ou and H Fan 2007 Phys. Rev. A 75 062308
[11]	Goura G, Bandyopadhyay S and Sanders B C 2007 J. Math. Phys. 48 012108
[12]	C Yu and H S Song 2008 Phys. Rev. A 77 032329
[13]	Kim J S, Das A and Sanders B C 2009 Phys. Rev. A 79 012329
[14]	Lee S and Park J 2009 Phys. Rev. A 79 054309
[15]	de Oliveira T R 2009 Phys. Rev. A 80 022331
[16]	Li Z G, Fei S M, Albeverio S and Liu W M 2009 Phys. Rev. A 80 034301
[17]	Cornelio M F and de Oliveira M C 2010 Phys. Rev. A 81 032332
[18]	Zhao M J, Fei S M and Wang Z X 2010 Int. J. Quant. Inform. 8 905
[19]	Seevinck M P 2010 Quantum Inf. Process 9 273
[20]	Li J J and Wang Z X 2010 Chin. Phys. B 19 100310
[21]	Man Z X, Xia Y J and An N B 2010 New J. Phys. 12 033020
[22]	Kim J S and Sanders B C 2011 J. Phys. A: Math. Theor. 44 295303
[23]	Giorgi G L 2011 Phys. Rev. A 84 054301
[24]	Prabhu R, Pati A K, Aditi Sen(De) and Ujwal Sen 2012 Phys. Rev. A 85 040102(R)
[25]	Sudha, Usha Devi A R and Rajagopal A K 2012 Phys. Rev. A 85 012103
[26]	Streltsov A, Adesso G, Piani M and Bruss D 2012 Phys. Rev. Lett. 109 050503
[27]	Fanchini F F, de Oliveira M C, Castelano L K and Cornelio M F 2013 Phys. Rev. A 87 032317
[28]	Ren X J and Fan H 2013 Quant. Inf. Comp. 13 0469
[29]	Liu S Y, Li B, Yang W L and Fan H 2013 Phys. Rev. A 87 062120
[30]	Bai Y K, Zhang N, YeMY and Wang Z D 2013 Phys. Rev. A 88 012123
[31]	Zhu X N and Fei S M 2014 Phys. Rev. A 90 024304
[32]	Zhu X N and Fei S M 2017 Quantum Inf Process
[33]	Salini K, Prabhu R, Aditi Sen(De) and Ujjwal S 2014 Ann. Phys. 348 297
[34]	Geetha P J, Sudha and Usha Devi A R 2014 J. Mod. Phys. 5 1294
[35]	Lohmayer R, Osterloh R A, Siewert J and Uhlmann A 2006 Phys. Rev. Lett. 97 260502
[36]	Bai Y K, Ye M Y and Wang Z D 2008 Phys. Rev. A 78 062325
[37]	Bai Y K, Xu Y F and Wang Z D 2014 Phys. Rev. Lett. 113 100503
[38]	Geetha P J, Yashodamma K O and Sudha 2015 Chin. Phys. B 24 110302
[39]	Peres A 1996 Phys. Rev. Lett. 77 1413
[40]	Horodecki M, Horodecki P and Horodecki R 1996 Phys. Lett. A 223 1
[41]	Vidal G and Werner R F 2002 Phys Rev. A 65 032314
[42]	Hill S and Wootters W K 1997 Phys. Rev. Lett. 78 5022
[43]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[44]	Majorana E 1932 Nuovo Cimento 9 43
[45]	Bastin T 2009 Phys. Rev. Lett. 103 070503
[46]	Usha Devi A R, Sudha and Rajagopal A K 2012 Quantum Inf. Process 11 685
[47]	Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314

[1]	Monogamous nature of symmetric N-qubit states of the W class: Concurrence and negativity tangle P. J. Geetha, K. O. Yashodamma, Sudha. Chin. Phys. B, 2015, 24(11): 110302.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Comparative analysis of entanglement measures based on monogamy inequality

Cite this article:

Online attention