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Volumn 62, Issue 3, 2000, Pages 1-10

Operational criterion and constructive checks for the separability of low-rank density matrices

Author keywords

[No Author keywords available]

Indexed keywords


EID: 18344371923     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (170)

References (38)
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    • A. Ekert, Phys. Rev. Lett. 67, 661 (1991); C. H. Bennett and S. J. Wiesner, ibid. 69, 2881 (1992); C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, ibid. 70, 1895 (1993).
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    • Ekert, A.1
  • 4
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    • A. Ekert, Phys. Rev. Lett. 67, 661 (1991); C. H. Bennett and S. J. Wiesner, ibid. 69, 2881 (1992); C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, ibid. 70, 1895 (1993).
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2881
    • Bennett, C.H.1    Wiesner, S.J.2
  • 18
    • 0000986501 scopus 로고    scopus 로고
    • G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999). See also S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. 83, 1054 (1999).
    • (1999) Phys. Rev. A , vol.59 , pp. 141
    • Vidal, G.1    Tarrach, R.2
  • 21
    • 18344396639 scopus 로고    scopus 로고
    • D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, e-print quant-ph/9908070; C. H. Bennett, D. P. DiVincenzo, Ch. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, e-print quant-ph/9804053. Also see R. Horodecki, M. Horodecki, and P. Horodecki, e-print quant-ph/9811004
    • C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 83, 3081 (1999); D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, e-print quant-ph/9908070; C. H. Bennett, D. P. DiVincenzo, Ch. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, e-print quant-ph/9804053. Also see R. Horodecki, M. Horodecki, and P. Horodecki, e-print quant-ph/9811004.
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 3081
    • Bennett, C.H.1    DiVincenzo, D.P.2    Mor, T.3    Shor, P.W.4    Smolin, J.A.5    Terhal, B.M.6
  • 22
    • 18344377001 scopus 로고    scopus 로고
    • B. Terhal, preprint, quant-ph/9810091
    • B. Terhal, preprint, quant-ph/9810091.
  • 24
    • 18344369763 scopus 로고    scopus 로고
    • B. Kraus, J. I. Cirac, S. Karnas, and M. Lewenstein, preprint, quant-ph/9912010. Also see M. Lewenstein, J. I. Cirac, and S. Karnas, e-print quant-ph/9903012
    • B. Kraus, J. I. Cirac, S. Karnas, and M. Lewenstein, preprint, quant-ph/9912010. Also see M. Lewenstein, J. I. Cirac, and S. Karnas, e-print quant-ph/9903012.
  • 26
    • 18344370106 scopus 로고    scopus 로고
    • note
    • Though the problem was reduced to the one-parameter question about one parameter Werner states [33], recent results strongly suggest that NPT BE states exist (W. Dür, I. Cirac, M. Lewenstein, and D. Bruß, e-print quant-ph/9910022); D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. Terhal, and A. Thapliyal, e-print quant-ph/9910026). The complete solution seems to be by no means trivial. It is only known that there are no PPT BE states in the 2 X N case [20].
  • 30
    • 18344391254 scopus 로고    scopus 로고
    • P. Horodecki, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, e-print quant-ph/9910122
    • P. Horodecki, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, e-print quant-ph/9910122.
  • 31
    • 85088488358 scopus 로고    scopus 로고
    • note
    • f〉 = 〈f|E-FF†|f〉≥0.
  • 33
    • 0003481878 scopus 로고
    • McGraw-Hill, New York
    • D. Luenberger, Introduction to Linear and Nonlinear Programming (Addison-Wesley, Reading, MA, 1984); D. Gale, The Theory of Linear Economic Models (McGraw-Hill, New York, 1960).
    • (1960) The Theory of Linear Economic Models
    • Gale, D.1
  • 34
    • 18344391910 scopus 로고    scopus 로고
    • unpublished
    • The generalization of this lemma to the case of continuous indices as well as its application, will be considered elsewhere [P. Horodecki, M. Lewenstein, M. Horodecki, R. Horodecki, (unpublished)].
    • Horodecki, P.1    Lewenstein, M.2    Horodecki, M.3    Horodecki, R.4
  • 35
    • 18344374543 scopus 로고    scopus 로고
    • D. P. DiVincenzo, B. M. Terhal, and A. V. Taphliyal, e-print quant-ph/9904005
    • D. P. DiVincenzo, B. M. Terhal, and A. V. Taphliyal, e-print quant-ph/9904005.
  • 37
    • 18344387957 scopus 로고    scopus 로고
    • P. Horodecki and M. Lewenstein, e-print quant-ph/0001035
    • P. Horodecki and M. Lewenstein, e-print quant-ph/0001035.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.