Abstract.
In this paper, an intuitive approach is employed to generalize the full separability criterion of tripartite quantum states of qubits to the higher-dimensional systems [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that less restrictive conditions are needed to characterize the properties of full separability. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and investigate the full separability of some weakly mixed states.
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References
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
M. Zukowski, A. Zeilinger, M.A. Horne, A.K. Ekert, Phys. Rev. Lett. 71, 4287 (1993)
C.H. Bennett et al., Phys. Rev. Lett. 70, 1895 (1993)
C.H. Bennett, S. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)
W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)
A. Uhlmann, Phys. Rev. A 62, 032307 (2000)
K. Audenaert, F. Verstraete, De Moor, Phys. Rev. A 64, 052304 (2001)
F. Mintert, M. Kuś, A. Buchleitner, Phys. Rev. Lett. 92, 167902 (2004)
V. Coffman, J. Kundu, W.K. Wootters, Phys. Rev. A 61, 052306 (2000)
W. Dür, G. Vidal, J.I. Cirac, Phys. Rev. A 62, 062314 (2000)
A. Miyake, Phys. Rev. A 67, 012108 (2003)
A. Osterloh, J. Siewert, Phys. Rev. A 72, 012337 (2005)
C.-S. Yu, H.-S. Song, Phys. Rev. A 73, 022325 (2006)
A.R.R. Carvalho, F. Mintert, A. Buchleitner, Phys. Rev. Lett. 93, 230501 (2004)
C.-S. Yu, H.-S. Song, Phys. Rev. A 72, 022333 (2005)
C.F. Van Loan, N.P. Pitsianis, in Linear Algebra for Large Scale and Real Time Applications, edited by M.S. Moonen, G. H. Golub (Kluwer, Dordrecht, 1993), pp. 293–314
N.P. Pitsianis, Ph.D. thesis, Cornell University, New York, 1997
A. Peres, Phys. Rev. Lett. 76, 1413 (1996)
H. Fan, e-print arXiv:quant-ph/0210168
R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, New York, 1985)
F. Mintert, A.R.R. Carvalho, M. Kuś, A. Buchleitner, Phys. Rep. 415, 207 (2005)
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Yu, CS., Song, HS. Full separability criterion for tripartite quantum systems. Eur. Phys. J. D 42, 147–151 (2007). https://doi.org/10.1140/epjd/e2006-00267-y
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DOI: https://doi.org/10.1140/epjd/e2006-00267-y
PACS.
- 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
- 03.67.Mn Entanglement production, characterization, and manipulation