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MAXIMIZING GENUINE MULTIPARTITE ENTANGLEMENT OF N MIXED QUBITS

Rochester Theory Center and the Department of Physics & Astronomy, University of Rochester, Rochester, New York 14627, USA

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and

SEYED MOHAMMAD HASHEMI RAFSANJANI

Rochester Theory Center and the Department of Physics & Astronomy, University of Rochester, Rochester, New York 14627, USA

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https://doi.org/10.1142/S0219749913500433Cited by:7 (Source: Crossref)

Abstract

Beyond the simplest case of bipartite qubits, the composite Hilbert space of multipartite systems is largely unexplored. In order to explore such systems, it is important to derive analytic expressions for parameters which characterize the system's state space. Two such parameters are the degree of genuine multipartite entanglement and the degree of mixedness of the system's state. We explore these two parameters for an N-qubit system whose density matrix has an X form. We derive the class of states that has the maximum amount of genuine multipartite entanglement for a given amount of mixedness. We compare our results with the existing results for the N = 2 case. The critical amount of mixedness above which no N-qubit X-state possesses genuine multipartite entanglement is derived. It is found that as N increases, states with higher mixedness can still be entangled.

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References

W. K. Wootters , Phys. Rev. Lett. 80 , 2245 ( 1998 ) . Web of Science, Google Scholar
A. Peres , Phys. Rev. Lett. 77 , 1413 ( 1996 ) . Web of Science, Google Scholar
M. Horodecki , P. Horodecki and R. Horodecki , Phys. Lett. A 223 , 1 ( 1996 ) . Web of Science, Google Scholar
M. Horodecki and P. Horodecki , Phys. Rev. A 59 , 4206 ( 1999 ) . Web of Science, Google Scholar
K. G. H. Vollbrecht and R. F. Werner , Phys. Rev. A 64 , 062307 ( 2001 ) . Web of Science, Google Scholar
R. Simon , Phys. Rev. Lett. 84 , 2726 ( 2000 ) . Web of Science, Google Scholar
R. Grobe , K. Rza̧zewski and J. H. Eberly , J. Phys. B 27 , L503 ( 1994 ) . Web of Science, Google Scholar
A. Ekert and P. L. Knight , Am. J. Phys. 63 , 415 ( 1995 ) . Web of Science, Google Scholar
O. Gühne and M. Seevinck , New J. Phys. 12 , 053002 ( 2010 ) . Web of Science, Google Scholar
Z. H. Ma et al. , Phys. Rev. A 83 , 062325 ( 2011 ) . Web of Science, Google Scholar
B. Jungnitsch , T. Moroder and O. Gühne , Phys. Rev. Lett. 106 , 190502 ( 2011 ) . Web of Science, Google Scholar
G. Tóth and O. Gühne , Phys. Rev. Lett. 94 , 060501 ( 2005 ) . Web of Science, Google Scholar
A. S. Villar et al. , Phys. Rev. Lett. 97 , 140504 ( 2006 ) . Web of Science, Google Scholar
G. Tóth et al. , New J. Phys. 11 , 083002 ( 2009 ) . Web of Science, Google Scholar
T. Gao and Y. Hong , Phys. Rev. A 82 , 062113 ( 2010 ) . Web of Science, Google Scholar
J.-D. Bancal et al. , Phys. Rev. Lett. 106 , 250404 ( 2011 ) . Web of Science, Google Scholar
M. Huber et al. , Phys. Rev. A 83 , 040301(R) ( 2011 ) . Web of Science, Google Scholar
S. M. Hashemi Rafsanjani et al. , Phys. Rev. A 86 , 062303 ( 2012 ) . Web of Science, Google Scholar
T. Yu and J. H. Eberly , Quantum Infor. Comput. 7 , 459 ( 2007 ) . Web of Science, Google Scholar
N. Quesada , A. Al-qasimi and D. F. V. James , J. Mod. Opt. 59 , 1322 ( 2012 ) . Web of Science, Google Scholar
S. M. Hashemi Rafsanjani and S. Agarwal, [quant-ph] , arXiv:1204.3912 . Google Scholar
W. J. Munro et al. , Phys. Rev. A 64 , 030302 ( 2001 ) . Web of Science, Google Scholar
T.-C. Wei et al. , Phys. Rev. A 67 , 022110 ( 2003 ) . Web of Science, Google Scholar
K. Źyczkowski et al. , Phys. Rev. A 58 , 883 ( 1998 ) . Web of Science, Google Scholar
S. Bose and V. Vedral , Phys. Rev. A 61 , 040101(R) ( 2000 ) . Web of Science, Google Scholar
G. Adesso , A. Serafini and F. Illuminati , Phys. Rev. Lett. 92 , 087901 ( 2004 ) . Web of Science, Google Scholar
A. Al-Qasimi and D. F. V. James , Phys. Rev. A 83 , 032101 ( 2011 ) . Web of Science, Google Scholar
N. D. Mermin , Phys. Rev. Lett. 65 , 1838 ( 1990 ) . Web of Science, Google Scholar
T. Monz et al. , Phys. Rev. Lett. 106 , 130506 ( 2011 ) . Web of Science, Google Scholar
L. S. Bishop et al. , New J. Phys. 11 , 073040 ( 2009 ) . Web of Science, Google Scholar
J. Grondalski , D. M. Etlinger and D. F. V. James , Phys. Lett. A 300 , 573 ( 2002 ) . Web of Science, Google Scholar