Abstract We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing, and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger-Horne-Zeilinger (GHZ) states and states, mixed with white noise, and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state (with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for are genuinely entangled.
(Entanglement measures, witnesses, and other characterizations)
Corresponding Authors:
Mazhar Ali
E-mail: mazharaliawan@yahoo.com
Cite this article:
Mazhar Ali Genuine entanglement under squeezed generalized amplitude damping channels with memory 2024 Chin. Phys. B 33 020307
[1] Wilde M M 2017 Quantum Information Theory (Cambridge: Cambridge Univ. Press) [2] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys.81 865 [3] Gühne O and Tóth G 2009 Phys. Rep.474 1 [4] Erhard M, Krenn M and Zeilinger A 2020 Nat. Rev. Phys.2 365 [5] Friis N, Vitagliano G, Malik M and Huber M 2019 Nat. Rev. Phys.1 72 [6] Ali M 2023 Quant. Infor. Process22 207 [7] Yu T and Eberly J H 2002 Phys. Rev. B66 193306 [8] Yu T and Eberly J H 2003 Phys. Rev. B68 165322 [9] Yu T and Eberly J H 2004 Phys. Rev. Lett.93 140404 [10] Eberly J H and Yu T 2007 Science316 555 [11] Dür W and Briegel H J 2004 Phys. Rev. Lett.92 180403 [12] Hein M, Dür W and Briegel H J 2005 Phys. Rev. A71 032350 [13] Aolita L, Chaves R, Cavalcanti D, Acín A and Davidovich L 2008 Phys. Rev. Lett.100 080501 [14] Simon C and Kempe J 2002 Phys. Rev. A65 052327 [15] Borras A, Majtey P, Plastino A R, Casas M and Plastino A 2009 Phys. Rev. A79 022108 [16] Cavalcanti D, Chaves R, Aolita L, Davidovich L and Acín A 2009 Phys. Rev. Lett.103 030502 [17] Bandyopadhyay S and Lidar D A 2005 Phys. Rev. A72 042339 [18] Chaves R and Davidovich L 2010 Phys. Rev. A82 052308 [19] Aolita L, Cavalcanti D, Chaves R, Dhara C, Davidovich L and Acín A 2010 Phys. Rev. A82 032317 [20] Carvalho A R R, Mintert F and Buchleitner A 2004 Phys. Rev. Lett.93 230501 [21] Lastra F, Romero G, Lopez C E, França Santos M and Retamal J C 2007 Phys. Rev A75 062324 [22] Gühne O, Bodoky F and Blaauboer M 2008 Phys. Rev. A78 060301 [23] López C E, Romero G, Lastra F, Solano E and Retamal J C 2008 Phys. Rev. Lett.101 080503 [24] Rau A R P, Ali M and Alber G 2008 Europhys. Lett.82 40002 [25] Ali M, Alber G and Rau A R P 2009 J. Phys. B: At. Mol. Opt. Phys.42 025501 [26] Ali M 2010 J. Phys. B: At. Mol. Opt. Phys.43 045504 [27] Ali M 2010 Phys. Rev. A81 042303 [28] Ali M and Gühne O 2014 J. Phys. B: At. Mol. Opt. Phys.47 055503 [29] Weinstein Y S, Feldman J, Robins J, Zukus J and Gilbert G 2012 Phys. Rev. A85 032324 [30] Filippov S N, Melnikov A A and Ziman M 2013 Phys. Rev. A88 062328 [31] Nielsen M A and Chuang I L 2010 Quantum Computation and Quantum Information (Cambridge: Cambridge Univ. Press) [32] Fujiwara A 2004 Phys. Rev. A70 012317 [33] Srikanth R and Banerjee S 2008 Phys. Rev. A77 012318 [34] Banerjee S and Ghosh R 2007 J. Phys. A: Math. Theor.40 13735 [35] Banaszek K, Dragan A, Wasilewski W and Radzewics C 2004 Phys. Rev. Lett.92 257901 [36] Plenio M B and Virmani S 2007 Phys. Rev. Lett.99 120504 [37] Daems D 2007 Phys. Rev. A76 012310 [38] D'Arrigo A, Benenti G, Falci G and Macchiavello C 2013 Phys. Rev. A88 042337 [39] Caruso F, Giovannetti V, Lupo C and Mancini S 2014 Rev. Mod. Phys.86 1203 [40] Guo Y N, Fang M F, Wang G Y and Zeng K 2016 Quant. Infor. Process.15 5129 [41] Ollivier H and Zurek W H 2001 Phys. Rev. Lett.88 017901 [42] Jeong Y and Shin H 2019 Scientific Reports9 4035 [43] Kim M S and Imoto N 1995 Phys. Rev. A52 2401 [44] Poyatos J F, Cirac J I and Zoller P 1996 Phys. Rev. Lett.77 4728 [45] Lütkenhaus N, Cirac J I and Zoller P 1998 Phys. Rev. A57 548 [46] Myatt C J, King B E, Turchette Q A, Sackett C A, Kielpinski D, Itano W M, Monroe C and Wineland D J 2000 Nature403 269 [47] Turchette Q A, Myatt C J, King B E, Sackett C A, Kielpinski D, Itano W M, Monroe C and Wineland D J 2000 Phys. Rev. A62 053807 [48] Wilson D, Lee J and Kim M S 2003 J. Mod. Opt.50 1809 [49] Banerjee S, Ravishankar V and Srikanth R 2010 Ann. Phys.325 816 [50] Orszag M 2016 Quantum Optics (Springer) [51] Scully M O and Zubairy M S 2001 Quantum Optics (Oxford University Press) [52] We figured out that Kraus operators provided in Ref. [42] have typos and also their number is 6. We provide here only 4 operators satisfying the standard restrictions on them. [53] Jungnitsch B, Moroder T and Gühne O 2011 Phys. Rev. Lett.106 190502 [54] Novo L, Moroder T and Gühne O 2013 Phys. Rev. A88 012305 [55] Hofmann M, Moroder T and Gühne O 2014 J. Phys. A: Math. Theor.47 155301 [56] Vidal G and Werner R F 2002 Phys. Rev. A65 032314 [57] Jungnitsch B, Moroder T and Gühne O 2011 Phys. Rev. A84 032310 [58] Rau A R P 2009 J. Phys. A: Math. Theor42 412002 [59] Gühne O and Seevinck M 2010 New. J. Phys.12 053002
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