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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 24, 2010

The checkerboard family of entangled states of two qutrits

Dragomir Ðoković EMAIL logo
From the journal Open Physics

Abstract

By modifying the method of Bruß and Peres, we construct two new families of entangled two qutrit states. For all density matrices ρ in these families we have ρ ij = 0 for i + j odd. The first family depends on 27 independent real parameters and includes both PPT and NPT states. The second family consists of PPT entangled states. The number of independent real parameters of this family is ≥ 11

[1] B. Baumgartner, B.C. Hiesmayr, H. Narnhofer, Phys. Rev. A 74, 032327 (2006) http://dx.doi.org/10.1103/PhysRevA.74.03232710.1103/PhysRevA.74.032327Search in Google Scholar

[2] B. Baumgartner, B.C. Hiesmayr, H. Narnhofer, Phys. Lett. A 372, 2190 (2008) http://dx.doi.org/10.1016/j.physleta.2007.11.02810.1016/j.physleta.2007.11.028Search in Google Scholar

[3] C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, B.M. Terhal, Phys. Rev. Lett. 82, 5385 (1999) http://dx.doi.org/10.1103/PhysRevLett.82.538510.1103/PhysRevLett.82.5385Search in Google Scholar

[4] W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry (Academic Press, New York, 1975) Search in Google Scholar

[5] D. Bruß, A. Peres, Phys. Rev. A 61, 030301(R) (2000) http://dx.doi.org/10.1103/PhysRevA.61.03030110.1103/PhysRevA.61.030301Search in Google Scholar

[6] J.I. de Vincente, Quantum Inf. Comput. 7, 624 (2007) 10.26421/QIC7.7-5Search in Google Scholar

[7] D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, B.M. Terhal, Commun. Math. Phys. 238, 379 (2003) http://dx.doi.org/10.1007/s00220-003-0877-610.1007/s00220-003-0877-6Search in Google Scholar

[8] K.-C. Ha, S.-H. Kye, J. Phys. A-Math. Gen. 38, 9039 (2005) http://dx.doi.org/10.1088/0305-4470/38/41/01410.1088/0305-4470/38/41/014Search in Google Scholar

[9] M. Horodecki, P. Horodecki, Phys. Rev. A 59, 4206 (1999) http://dx.doi.org/10.1103/PhysRevA.59.420610.1103/PhysRevA.59.4206Search in Google Scholar

[10] M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996) http://dx.doi.org/10.1016/S0375-9601(96)00706-210.1016/S0375-9601(96)00706-2Search in Google Scholar

[11] M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998) http://dx.doi.org/10.1103/PhysRevLett.80.523910.1103/PhysRevLett.80.5239Search in Google Scholar

[12] M. Horodecki, P. Horodecki, R. Horodecki, In G. Alber et al. (Ed.), Quantum Information Theory: An Intro- duction to Basic Theoretical Concepts and Experiments, Springer Tracts in Modern Physics Vol. 173 (Springer Verlag, Berlin, 2001) 151 Search in Google Scholar

[13] P. Horodecki, Phys. Lett. A 232, 333 (1997) http://dx.doi.org/10.1016/S0375-9601(97)00416-710.1016/S0375-9601(97)00416-7Search in Google Scholar

[14] W.C. Kim, S.-H. Kye, Phys. Lett. A 369, 16 (2007) http://dx.doi.org/10.1016/j.physleta.2007.04.06210.1016/j.physleta.2007.04.062Search in Google Scholar

[15] A. Peres, Phys. Rev. Lett. 77, 1413 (1996) http://dx.doi.org/10.1103/PhysRevLett.77.141310.1103/PhysRevLett.77.1413Search in Google Scholar PubMed

[16] P.W. Shor, J.A. Smolin, B.M. Terhal, Phys. Rev. Lett. 86, 2681 (2001) http://dx.doi.org/10.1103/PhysRevLett.86.268110.1103/PhysRevLett.86.2681Search in Google Scholar PubMed

Published Online: 2010-9-24
Published in Print: 2011-2-1

© 2010 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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