Abstract
We develop separability criteria to identify non-k-separability (k = 2,3, ... ,n) and genuine multipartite entanglement in different classes of mixed n-partite quantum states using elements of density matrices. With the help of these criteria, we detect non-k-separability in n-qudit GHZ and W states respectively added with white noise. We also discuss the experimental implementation of our criteria by means of local observables.
Graphical abstract
Similar content being viewed by others
References
R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)
O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009)
R. Jozsa, N. Linden, Proc. R. Soc. A 459, 2011 (2003)
A. Karlsson, M. Bourennane, Phys. Rev. A 58, 4394 (1998)
M. Hillery, V. Bužek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999)
P. Agrawal, A. Pati, Phys. Rev. A 74, 062320 (2006)
S.-B. Zheng, Phys. Rev. A 74, 054303 (2006)
E. D’Hondt, P. Panangaden, Quantum Inf. Comput. 6, 173 (2006).
D.M. Greenberger, M.A. Horne, A. Shimony, A. Zeilinger, Am. J. Phys. 58, 1131 (1990)
J.D. Bancal, C. Branciard, N. Gisin, S. Pironio, Phys. Rev. Lett. 103, 090503 (2009)
A. Cabello, Phys. Rev. A 65, 032108 (2002)
A. Gabriel, B.C. Hiesmeyr, M. Huber, Quantum Inf. Comput. 10, 0829 (2010)
W. Dür, J.I. Cirac, R. Tarrach, Phys. Rev. Lett. 83, 3562 (1999)
W. Dür, J.I. Cirac, Phys. Rev. A 61, 042314 (2000)
W. Dür, J.I. Cirac, J. Phys. A 34, 6837 (2001)
M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89, 060401 (2002)
J. Uffink, Phys. Rev. Lett. 88, 230406 (2002)
W. Laskowski, M. Zukowski, Phys. Rev. A 72, 062112 (2005)
G. Tóth, O. Gühne, Phys. Rev. A 72, 022340 (2005)
M. Seevinck, J. Uffink, Phys. Rev. A 78, 032101 (2008)
M. Huber, F. Mintert, A. Gabriel, B.C. Hiesmeyr, Phys. Rev. Lett. 104, 210501 (2010)
T. Gao, Y. Hong, Phys. Rev. A 82, 062113 (2010)
O. Gühne, M. Seevinck, New J. Phys. 12, 053002 (2010)
T. Gao, Y. Hong, Eur. Phys. J. D 61, 765 (2011)
T. Gao, Y. Hong, Y. Lu, F. Yan, Europhys. Lett. 104, 20007 (2013)
O. Gühne, C.-Y. Lu, W.-B. Gao, J.-W. Pan, Phys. Rev. A 76, 030305(R) (2007)
Y. Lu, G.L. Long, T. Gao, Int. J. Theor. Phys. 52, 699 (2013)
J.S. Kim, B.C. Sanders, J. Phys. A 41, 495301 (2008)
M. Huber, M.P. Llobet, J.I. de Vicente, Phys. Rev. A 88, 042328 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ananth, N., Chandrasekar, V.K. & Senthilvelan, M. Criteria for non-k-separability of n-partite quantum states. Eur. Phys. J. D 69, 56 (2015). https://doi.org/10.1140/epjd/e2015-50538-5
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2015-50538-5