Abstract.
We address the dynamics of decoherence and quantum correlations (entanglement and discord) in a model of three non-interacting qubits, initially prepared in a maximally entangled pure Greenberger-Horne-Zeilinger (GHZ) state and then subjected to classical environmental noise in common, different and mixed environments. The noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and colored environmental noise. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the kind of the noise considered. On the one hand, our results clearly show that unlike what was found in the case of the two-qubit model analogous to the one here investigated, quantum correlations are not totally destroyed when the qubits are coupled to the noise in a common environment. On the other hand, the presence or absence of peculiar phenomena, such as entanglement, revivals and sudden death are observed. Furthermore, we show that the partial preservation of entanglement can be successfully detected by means of the suitable entanglement witness. Finally, in the case of static noise we find that the decoherence becomes stronger as the disorder of the environment increases whereas, for colored noise, it becomes stronger as the number of fluctuators increases.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
M. Ramzan, Eur. Phys. J. D 67, 170 (2013)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2010)
J.I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995)
C.H. Bennett, D.P. DiVincenzo, Nature 404, 247 (2000)
C. Xie, Y. Liu, H. Xing et al., Quantum Inf. Process. 14, 653 (2015)
N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002)
X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, K. Peng, Phys. Rev. Lett. 88, 04790416 (2002)
Th. Richter, W. Vogel, Phys. Rev. A 76, 053835 (2012)
M. Murao, D. Jonathan, M.B. Plenio, V. Vedral, Phys. Rev. A 59, 156 (1999)
C.Y. Hu, J.G. Rarity, Phys. Rev. B 83, 115303 (2011)
T. Yu, J.H. Eberly, Science 323, 598 (2009)
L. Aolita, F. de Melo, L. Davidovich, Rep. Prog. Phys. 78, 042001 (2015)
R. Lo Franco, Quantum Inf. Process. 15, 2393 (2016)
T. Yu, J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004)
N. Metwally, A.S. Obada, arXiv:1506.01036 (2015)
C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Int. J. Quant. Inf. 10, 1241005 (2012)
C. Benedetti, M.G.A. Paris, F. Buscemi, P. Bordone, Time-evolution of entanglement and quantum discord of bipartite systems subject to $1/f^{\alpha}$ noise, in Proceedings of the 22nd International Conference on Noise and Fluctuations (ICNF) 2013 Montpellier (IEEE, 2013) DOI:10.1109/ICNF.2013.6578952
D. Zhou, A. Lang, R. Joynt, Quantum Inf. Process. 9, 727 (2010)
A. De, A. Lang, D. Zhou, R. Joynt, Phys. Rev. A 83, 042331 (2011)
B. Leggio, R. Lo Franco, D.O. Soares-Pinto, P. Horodecki, G. Compagno, Phys. Rev. A 92, 032311 (2015)
A. D’Arrigo, G. Benenti, R. Lo Franco, G. Falci, E. Paladino, Int. J. Quant. Inf. 12, 1461005 (2014)
J.-S. Xu, K. Sun, C.-F. Li et al., Nat. Commun. 4, 2851 (2013)
A. Orieux, A. D’Arrigo, G. Ferranti, R.L. Franco et al., Sci. Rep. 5, 8575 (2015)
F. Buscemi, P. Bordone, Phys. Rev. A 87, 042310 (2013)
W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)
M.C. Tichy, F. Mintert, A. Buchleitner, J. Phys. B: At. Mol. Opt. Phys. 44, 192001 (2011)
R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)
L. Gurvits, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing (AMC, New York, 2003) pp. 10--19
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
Z.H. Chen, Z.H. Ma, J.L. Chen, S. Severini, Phys. Rev. A 85, 062320 (2012)
Y.S. Weinstein, Phys. Rev. A 79, 012318 (2009)
A. Acin, A. Andrianov, L. Costa, E. Jan, J.I. Latorre, R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000)
C.H. Bennett, D.P. DiVincenzo, C.A. Fuchs et al., Phys. Rev. A 59, 1070 (1999)
M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen, U. Sen, B. Synak-Radtke, Phys. Rev. A 71, 062307 (2005)
J. Niset, N.J. Cerf, Phys. Rev. A 74, 052103 (2006)
J. Cui, H. Fan, J. Phys. A 43, 045305 (2010)
B.P. Lanyon, M. Barbieri, M.P. Almeida, A.G. White, Phys. Rev. Lett. 101, 200501 (2008)
Z. Jian-Song, C. Ai-Xi, Quant. Phys. Lett. 69, 1 (2012)
K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)
S. Luo, Phys. Rev. A 77, 022301 (2008)
J. Maziero, L.C. C’eleri, R.M. Serra, V. Vedral, Phys. Rev. A 80, 044102 (2009)
T. Werlang, S. Souza, F.F. Fanchini, C.J. Villas Boas, Phys. Rev. A 80, 024103 (2009)
L. Mazzola, J. Piilo, S. Maniscalco, Phys. Rev. Lett. 104, 200401 (2010)
J.-S. Xu, X.-Ye. Xu, C.-F. Li et al., Nat. Commun. 1, 7 (2010)
M. Cianciaruso, T.R. Bromley, W. Roga, R. Lo Franco, G. Adesso, Sci. Rep. 5, 10177 (2015)
B. Aaronson, R. Lo Franco, G. Adesso, Phys. Rev. A 88, 012120 (2013)
M.B. Weissman, Rev. Mod. Phys. 60, 537 (1988)
G. Falci, A. D’arrigo, A. Mastellone, E. Paladino, Phys. Rev. Lett. 94, 167002 (2005)
B. Bellomo, G. Compagno, A. D’Arrigo, G. Falci, R. Lo Franco, E. Paladino, Phys. Rev. A 81, 062309 (2010)
C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 87, 052328 (2013)
G.L. Giorgi, B. Bellomo, F. Galve, R. Zambrini, Phys. Rev. Lett. 107, 190501 (2011)
C. Sabin, G. Garcia-Alcaine, Eur. Phys. J. D 48, 435 (2008)
G.N. Matthew, PhD Thesis, University of California, Santa Barbara (2010)
A. Acin, D. Bruss, M. Lewenstein, A. Sanpera, Phys. Rev. Lett. 87, 040401 (2001)
S. Bose, V. Vedral, Phys. Rev. A 61, 040101 (2000)
A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1998)
C.H. Bennett, A. Grudka, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 83, 012312 (2011)
L. Zhao, X. Hu, R. Yue et al., Quantum Inf. Process. 12, 2371 (2013)
A. Beggi, F. Buscemi, P. Bordone, Quantum Inf. Process. 14, 573 (2015)
P. Bordone, F. Buscemi, C. Benedetti, Fluctuat. Noise Lett. 11, 1242003 (2012)
E. Paladino, A. DArrigo, A. Mastellone, G. Falci, New J. Phys. 13, 093037 (2011)
J. Bergli, Y.M. Galperin, B.L. Altshuler, New J. Phys. 11, 025002 (2009)
B. Abel, F. Marquardt, Phys. Rev. B 78, 201302 (2008)
Z. Zhu-Qiang, W. An-Min, Q. Liang, Commun. Theor. Phys. 50, 1123 (2008)
J. Ma, Z. Sun, X. Wang, F. Nori, Phys. Rev. A 85, 062323 (2012)
Z.-X. Man, Y.-J. Xia, R. Lo Franco, Sci. Rep. 5, 13843 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tchoffo, M., Kenfack, L., Fouokeng, G. et al. Quantum correlations dynamics and decoherence of a three-qubit system subject to classical environmental noise. Eur. Phys. J. Plus 131, 380 (2016). https://doi.org/10.1140/epjp/i2016-16380-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2016-16380-3