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Volumn 69, Issue 2, 2004, Pages 223081-2230820

Complete family of separability criteria

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA PROCESSING; ENTROPY; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; TENSORS; VECTORS;

EID: 1942476085     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (372)

References (54)
  • 7
    • 0001106658 scopus 로고    scopus 로고
    • Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, edited by G. Alber et al. (Springer Verlag, Berlin)
    • 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.
    • (2001) Springer Tracts in Modern Physics , vol.173 , pp. 151-195
    • Horodecki, M.1    Horodecki, P.2    Horodecki, R.3
  • 29
    • 85015766797 scopus 로고    scopus 로고
    • A. Y. Kitaev, URL http://www.msri.org/publications/In/msri/2002/qip/ kitaev/1/
    • Kitaev, A.Y.1
  • 30
    • 85015801660 scopus 로고    scopus 로고
    • A. Ambainis, H. Buhrman, Y. Dodis, and H. Roehrig, e-print quant-ph/0304112
    • A. Ambainis, H. Buhrman, Y. Dodis, and H. Roehrig, e-print quant-ph/0304112.
  • 38
    • 85015716855 scopus 로고    scopus 로고
    • private communication
    • B. Schumacher (private communication).
    • Schumacher, B.1
  • 40
    • 85015789764 scopus 로고    scopus 로고
    • note
    • 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
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970).
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 45
    • 85015771428 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri (unpublished)
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri (unpublished).
  • 48
    • 84974621399 scopus 로고    scopus 로고
    • private communication
    • N. Gisin (private communication). For the intuition behind this state, see N. Gisin and S. Wolf, Lect. Notes Comput. Sci. 1880, 482 (2000); R. Renner and S. Wolf ibid. 2656, 562 (2003).
    • Gisin, N.1
  • 49
    • 84974621399 scopus 로고    scopus 로고
    • N. Gisin (private communication). For the intuition behind this state, see N. Gisin and S. Wolf, Lect. Notes Comput. Sci. 1880, 482 (2000); R. Renner and S. Wolf ibid. 2656, 562 (2003).
    • (2000) Lect. Notes Comput. Sci. , vol.1880 , pp. 482
    • Gisin, N.1    Wolf, S.2
  • 50
    • 35248888499 scopus 로고    scopus 로고
    • N. Gisin (private communication). For the intuition behind this state, see N. Gisin and S. Wolf, Lect. Notes Comput. Sci. 1880, 482 (2000); R. Renner and S. Wolf ibid. 2656, 562 (2003).
    • (2003) Lect. Notes Comput. Sci. , vol.2656 , pp. 562
    • Renner, R.1    Wolf, S.2
  • 51
    • 85015790971 scopus 로고    scopus 로고
    • private communication
    • B. Reznick (private communication).
    • Reznick, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.