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Volumn 69, Issue 2, 2004, Pages 20-

Complete family of separability criteria

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Indexed keywords


EID: 85037251019     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.69.022308     Document Type: Article
Times cited : (61)

References (53)
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    • M. N. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
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    • M. Horodecki, P. Horodecki, and R. Horodecki, in Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, edited by G. Alber et al., Springer Tracts in Modern Physics Vol. 173 (Springer Verlag, Berlin, 2001), pp. 151–195
    • M. Horodecki, P. Horodecki, and R. Horodecki, in Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, edited by G. Alber et al., Springer Tracts in Modern Physics Vol. 173 (Springer Verlag, Berlin, 2001), pp. 151–195.
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    • L. Gurvits, in Proceedings of the Thirty-fifth ACM Symposium on Theory of Computing (ACM Press, New York, 2003), pp. 10–19
    • L. Gurvits, in Proceedings of the Thirty-fifth ACM Symposium on Theory of Computing (ACM Press, New York, 2003), pp. 10–19.
  • 22
    • 85037207952 scopus 로고    scopus 로고
    • J. Bochnak, M. Coste, and M.-F. Roy, Real Algebraic Geometry (Springer, Berlin, 1998)
    • J. Bochnak, M. Coste, and M.-F. Roy, Real Algebraic Geometry (Springer, Berlin, 1998).
  • 26
    • 85037212524 scopus 로고    scopus 로고
    • L. Vandenberghe and S. Boyd, URL http://www.standford.edu/∼boyd/cvxbook.html
    • L. Vandenberghe and S. Boyd, URL http://www.standford.edu/∼boyd/cvxbook.html
  • 29
    • 85037188652 scopus 로고    scopus 로고
    • A. Y. Kitaev, URL http://www.msri.org/publications/In/msri/2002/qip/kitaev/1
    • A. Y. Kitaev, URL http://www.msri.org/publications/In/msri/2002/qip/kitaev/1
  • 38
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    • B. Schumacher (private communication)
    • B. Schumacher (private communication).
  • 40
    • 85037186512 scopus 로고    scopus 로고
    • To see why this is possible, consider the basis of positive semidefinite operators introduced in Sec. IV of Ref. 39. Since these operators are PSD each one can be made positive by adding an arbitrarily small multiple of the identity. But performing arbitrarily small changes to a set of linearly independent vectors does not affect its linear independence. Hence, we can replace each PSD operator of the set by a positive definite (but non-orthogonal) one and still have a basis of the whole vector space
    • To see why this is possible, consider the basis of positive semidefinite operators introduced in Sec. IV of Ref. 39. Since these operators are PSD each one can be made positive by adding an arbitrarily small multiple of the identity. But performing arbitrarily small changes to a set of linearly independent vectors does not affect its linear independence. Hence, we can replace each PSD operator of the set by a positive definite (but non-orthogonal) one and still have a basis of the whole vector space.
  • 42
    • 85037217722 scopus 로고    scopus 로고
    • R. T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970)
    • R. T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970).
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    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri (unpublished)
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri (unpublished).
  • 46
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    • J. Sturm, SeDuMi version 1.05, available from URL http://fewcal.kub.nl/sturm/software/sedumi.html
    • J. Sturm, SeDuMi version 1.05, available from URL http://fewcal.kub.nl/sturm/software/sedumi.html
  • 47
    • 85037209576 scopus 로고    scopus 로고
    • F. M. Spedalieri, P. A. Parrilo, and A. C. Doherty, MATLAB Code for Separability Tests, URL http://www.iqi.caltech.edu/publications.html
    • F. M. Spedalieri, P. A. Parrilo, and A. C. Doherty, MATLAB Code for Separability Tests, URL http://www.iqi.caltech.edu/publications.html
  • 48
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    • N. Gisin (private communication). For the intuition behind this state, see N. Gisin and S. Wolf, Lect. Notes Comput. Sci. 1880, 482 (2000)
    • (2000) Lect. Notes Comput. Sci. , vol.1880 , pp. 482
    • Gisin, N.1    Wolf, S.2
  • 49
    • 35248888499 scopus 로고    scopus 로고
    • R. Renner and S. Wolf 2656, 562 (2003).
    • (2003) , vol.2656 , pp. 562
    • Renner, R.1    Wolf, S.2
  • 50
    • 85037241356 scopus 로고    scopus 로고
    • B. Reznick (private communication)
    • B. Reznick (private communication).
  • 52
    • 85037253601 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, in Proceedings of QCMC 2002, edited by J. H. Shapiro and O. Hirota (Rinton Press, Princeton, 2003)
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, in Proceedings of QCMC 2002, edited by J. H. Shapiro and O. Hirota (Rinton Press, Princeton, 2003).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.