메뉴 건너뛰기




Volumn 70, Issue 2, 2004, Pages

Entropic uncertainty relations and entanglement

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CORRELATION METHODS; CRYPTOGRAPHY; EIGENVALUES AND EIGENFUNCTIONS; ENTROPY; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; UNCERTAIN SYSTEMS;

EID: 19544375232     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.022316     Document Type: Article
Times cited : (152)

References (69)
  • 3
    • 0000234949 scopus 로고
    • H. P. Robertson, Phys. Rev. 34, 163 (1929); 46, 794 (1934).
    • (1934) Phys. Rev. , vol.46 , pp. 794
  • 5
    • 33749331646 scopus 로고
    • I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975); D. Deutsch, Phys. Rev. Lett. 50, 631 (1983); K. Kraus, Phys. Rev. D 35, 3070 (1987).
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 631
    • Deutsch, D.1
  • 6
    • 0000548095 scopus 로고
    • I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975); D. Deutsch, Phys. Rev. Lett. 50, 631 (1983); K. Kraus, Phys. Rev. D 35, 3070 (1987).
    • (1987) Phys. Rev. D , vol.35 , pp. 3070
    • Kraus, K.1
  • 7
    • 0001287029 scopus 로고
    • H. Maassen and J. B.M. Uffink, Phys. Rev. Lett. 60, 1103 (1988); see also H. Maassen, in Quantum Probability and Applications V, edited by L. Accardi and W. von Waldenfels, Lecture Notes in Mathematics Vol. 1442 (Springer, Berlin, 1988), p. 263.
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 1103
    • Maassen, H.1    Uffink, J.B.M.2
  • 8
    • 0001287029 scopus 로고
    • edited by L. Accardi and W. von Waldenfels, Lecture Notes in Mathematics (Springer, Berlin)
    • H. Maassen and J. B.M. Uffink, Phys. Rev. Lett. 60, 1103 (1988); see also H. Maassen, in Quantum Probability and Applications V, edited by L. Accardi and W. von Waldenfels, Lecture Notes in Mathematics Vol. 1442 (Springer, Berlin, 1988), p. 263.
    • (1988) Quantum Probability and Applications V , vol.1442 , pp. 263
    • Maassen, H.1
  • 9
    • 11744373290 scopus 로고
    • E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23, 823 (1935); 23, 844 (1935); A. Einstein, N. Podolski, and N. Rosen, Phys. Rev. 47, 777 (1935).
    • (1935) Naturwissenschaften , vol.23 , pp. 807
    • Schrödinger, E.1
  • 10
    • 18144427760 scopus 로고
    • E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23, 823 (1935); 23, 844 (1935); A. Einstein, N. Podolski, and N. Rosen, Phys. Rev. 47, 777 (1935) .
    • (1935) Naturwissenschaften , vol.23 , pp. 823
  • 11
    • 2542427703 scopus 로고
    • E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23, 823 (1935); 23, 844 (1935); A. Einstein, N. Podolski, and N. Rosen, Phys. Rev. 47, 777 (1935) .
    • (1935) Naturwissenschaften , vol.23 , pp. 844
  • 12
    • 33947385649 scopus 로고
    • E. Schrödinger, Naturwissenschaften 23, 807 (1935); 23, 823 (1935); 23, 844 (1935); A. Einstein, N. Podolski, and N. Rosen, Phys. Rev. 47, 777 (1935) .
    • (1935) Phys. Rev. , vol.47 , pp. 777
    • Einstein, A.1    Podolski, N.2    Rosen, N.3
  • 13
    • 0343152990 scopus 로고
    • A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991); C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993) .
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 661
    • Ekert, A.K.1
  • 15
    • 4243217780 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002); O. Rudolph, Phys. Rev. A 67, 032312 (2003); K. Chen and L. Wu, Quantum Inf. Comput. 3, 193 (2003); M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008; A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004); for a review, see D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 187904
    • Doherty, A.C.1    Parrilo, P.A.2    Spedalieri, F.M.3
  • 16
    • 0037837547 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002); O. Rudolph, Phys. Rev. A 67, 032312 (2003); K. Chen and L. Wu, Quantum Inf. Comput. 3, 193 (2003); M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008; A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004); for a review, see D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002).
    • (2003) Phys. Rev. A , vol.67 , pp. 032312
    • Rudolph, O.1
  • 17
    • 0141752800 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002); O. Rudolph, Phys. Rev. A 67, 032312 (2003); K. Chen and L. Wu, Quantum Inf. Comput. 3, 193 (2003); M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008; A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004); for a review, see D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002).
    • (2003) Quantum Inf. Comput. , vol.3 , pp. 193
    • Chen, K.1    Wu, L.2
  • 18
    • 4243217780 scopus 로고    scopus 로고
    • M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002); O. Rudolph, Phys. Rev. A 67, 032312 (2003); K. Chen and L. Wu, Quantum Inf. Comput. 3, 193 (2003); M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008; A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004); for a review, see D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002).
  • 19
    • 1942476085 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002); O. Rudolph, Phys. Rev. A 67, 032312 (2003); K. Chen and L. Wu, Quantum Inf. Comput. 3, 193 (2003); M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008; A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004); for a review, see D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002).
    • (2004) Phys. Rev. A , vol.69 , pp. 022308
    • Doherty, A.C.1    Parrilo, P.A.2    Spedalieri, F.M.3
  • 20
    • 0038288033 scopus 로고    scopus 로고
    • A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002); O. Rudolph, Phys. Rev. A 67, 032312 (2003); K. Chen and L. Wu, Quantum Inf. Comput. 3, 193 (2003); M. Horodecki, P. Horodecki, and R. Horodecki, e-print quant-ph/0206008; A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004); for a review, see D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002).
    • (2002) J. Mod. Opt. , vol.49 , pp. 1399
    • Bruß, D.1    Cirac, J.I.2    Horodecki, P.3    Hulpke, F.4    Kraus, B.5    Lewenstein, M.6    Sanpera, A.7
  • 21
    • 33144464884 scopus 로고
    • M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, ibid. 84, 2722 (2000); S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, ibid. 88, 120401 (2002); P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003); G. Tóth, C. Simon, and J. I. Cirac, ibid. 68, 062310 (2003).
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 2731
    • Reid, M.D.1    Drummond, P.D.2
  • 22
    • 0000693787 scopus 로고    scopus 로고
    • M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, ibid. 84, 2722 (2000); S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, ibid. 88, 120401 (2002); P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003); G. Tóth, C. Simon, and J. I. Cirac, ibid. 68, 062310 (2003).
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 2722
    • Duan, L.-M.1    Giedke, G.2    Cirac, J.I.3    Zoller, P.4
  • 23
    • 0037171166 scopus 로고    scopus 로고
    • M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, ibid. 84, 2722 (2000); S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, ibid. 88, 120401 (2002); P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003); G. Tóth, C. Simon, and J. I. Cirac, ibid. 68, 062310 (2003).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 120401
    • Mancini, S.1    Giovannetti, V.2    Vitali, D.3    Tombesi, P.4
  • 24
    • 0038106466 scopus 로고    scopus 로고
    • M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, ibid. 84, 2722 (2000); S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, ibid. 88, 120401 (2002); P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003); G. Tóth, C. Simon, and J. I. Cirac, ibid. 68, 062310 (2003).
    • (2003) Phys. Rev. A , vol.67 , pp. 052315
    • Van Loock, P.1    Furusawa, A.2
  • 25
    • 1142280242 scopus 로고    scopus 로고
    • M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, ibid. 84, 2722 (2000); S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, ibid. 88, 120401 (2002); P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003); G. Tóth, C. Simon, and J. I. Cirac, ibid. 68, 062310 (2003).
    • (2003) Phys. Rev. A , vol.68 , pp. 062310
    • Tóth, G.1    Simon, C.2    Cirac, J.I.3
  • 27
    • 0242442484 scopus 로고    scopus 로고
    • H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003); H. F. Hofmann, ibid. 68, 034307 (2003) .
    • (2003) Phys. Rev. A , vol.68 , pp. 034307
    • Hofmann, H.F.1
  • 32
    • 0000353513 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (1996) Phys. Lett. A , vol.210 , pp. 377
    • Horodecki, R.1    Horodecki, P.2    Horodecki, M.3
  • 33
    • 0001339646 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (1996) Phys. Rev. A , vol.54 , pp. 1838
    • Horodecki, R.1    Horodecki, M.2
  • 34
    • 6144253009 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 5194
    • Cerf, N.J.1    Adami, C.2
  • 35
    • 0001162968 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (1999) Phys. Lett. A , vol.260 , pp. 335
    • Vidiella-Barranco, A.1
  • 36
    • 0035157443 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (2001) Physica A , vol.289 , pp. 157
    • Abe1    Rajagopal, A.K.2
  • 37
    • 4244020670 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (2001) Phys. Rev. A , vol.63 , pp. 042104
    • Tsallis, C.1    Lloyd, S.2    Baranger, M.3
  • 38
    • 0035981730 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (2002) J. Math. Phys. , vol.43 , pp. 4299
    • Vollbrecht, K.G.H.1    Wolf, M.M.2
  • 39
    • 1942443833 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (2004) Phys. Rev. A , vol.69 , pp. 022317
    • Mintert, F.1    Zyczkowski, K.2
  • 40
    • 0035963009 scopus 로고    scopus 로고
    • See, e.g., R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996); R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838 (1996); N. J. Cerf and C. Adami, Phys. Rev. Lett. 79, 5194 (1997); A. Vidiella-Barranco, Phys. Lett. A 260, 335 (1999); S. Abe and A. K. Rajagopal, Physica A 289, 157 (2001); C. Tsallis, S. Lloyd, and M. Baranger, Phys. Rev. A 63, 042104 (2001); K. G. H. Vollbrecht and M. M. Wolf, J. Math. Phys. 43, 4299 (2002); F. Mintert and K. Życzkowski, Phys. Rev. A 69, 022317 (2004); some of these results follow from a majorization relation proven in M. A. Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001).
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 5184
    • Nielsen, M.A.1    Kempe, J.2
  • 44
    • 5444243661 scopus 로고
    • Tankönyvkiadó, Budapest
    • A. Rényi, Valószínuségszámítás (Tankönyvkiadó, Budapest, 1966) [English translation: Probability Theory (North-Holland, Amsterdam, 1970)].
    • (1966) Valószínuségszámítás
    • Rényi, A.1
  • 45
    • 0003981318 scopus 로고
    • North-Holland, Amsterdam
    • A. Rényi, Valószínuségszámítás (Tankönyvkiadó, Budapest, 1966) [English translation: Probability Theory (North-Holland, Amsterdam, 1970)].
    • (1970) Probability Theory
  • 46
    • 5844266551 scopus 로고
    • A. Wehrl, Rev. Mod. Phys. 50, 221 (1978); for results on the relationships between the different entropies, see also, K. Życzkowski, Open Syst. Inf. Dyn. 10, 297 (2003).
    • (1978) Rev. Mod. Phys. , vol.50 , pp. 221
    • Wehrl, A.1
  • 47
    • 0347585673 scopus 로고    scopus 로고
    • A. Wehrl, Rev. Mod. Phys. 50, 221 (1978); for results on the relationships between the different entropies, see also, K. Życzkowski, Open Syst. Inf. Dyn. 10, 297 (2003).
    • (2003) Open Syst. Inf. Dyn. , vol.10 , pp. 297
    • Zyczkowski, K.1
  • 48
    • 85015781030 scopus 로고    scopus 로고
    • note
    • Note that the sign "≻" is sometimes defined the other way round in the literature.
  • 49
    • 0037193032 scopus 로고    scopus 로고
    • N. Canosa and R. Rossignoli, Phys. Rev. Lett. 88, 170401 (2002); R. Rossignoli and N. Canosa, Phys. Rev. A 66, 042306 (2002).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 170401
    • Canosa, N.1    Rossignoli, R.2
  • 50
    • 0036818959 scopus 로고    scopus 로고
    • N. Canosa and R. Rossignoli, Phys. Rev. Lett. 88, 170401 (2002); R. Rossignoli and N. Canosa, Phys. Rev. A 66, 042306 (2002).
    • (2002) Phys. Rev. A , vol.66 , pp. 042306
    • Rossignoli, R.1    Canosa, N.2
  • 57
    • 4043120596 scopus 로고    scopus 로고
    • T.-C. Wei and P. M. Goldbart, Phys. Rev. A 68, 042307 (2003); M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, Phys. Rev. Lett. 92, 087902 (2004).
    • (2003) Phys. Rev. A , vol.68 , pp. 042307
    • Wei, T.-C.1    Goldbart, P.M.2
  • 60
    • 0001339646 scopus 로고    scopus 로고
    • This geometrical picture was also studied in R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838, (1996); R. A. Bertlmann, H. Narnhofer, and W. Thirring, ibid 66, 032319 (2002).
    • (1996) Phys. Rev. A , vol.54 , pp. 1838
    • Horodecki, R.1    Horodecki, M.2
  • 61
    • 0036756837 scopus 로고    scopus 로고
    • This geometrical picture was also studied in R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838, (1996); R. A. Bertlmann, H. Narnhofer, and W. Thirring, ibid 66, 032319 (2002).
    • (2002) Phys. Rev. A , vol.66 , pp. 032319
    • Bertlmann, R.A.1    Narnhofer, H.2    Thirring, W.3
  • 62
    • 0141782139 scopus 로고    scopus 로고
    • An entanglement witness script W sign is an observable with the property Tr(script W sign) ≥ 0 for all separable states and Tr(script W sign) < 0 for some entangled states. See, e.g., M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000).
    • (2000) Phys. Rev. A , vol.62 , pp. 052310
    • Lewenstein, M.1    Kraus, B.2    Cirac, J.I.3    Horodecki, P.4
  • 66
    • 85015714961 scopus 로고    scopus 로고
    • G. Tóth (private communication); see also, V. Scarani, A. Acín, E. Schenck, and M. Aspelmeyer, e-print quant-ph/0405119;
    • G. Tóth (private communication); see also, V. Scarani, A. Acín, E. Schenck, and M. Aspelmeyer, e-print quant-ph/0405119; G. Tóth and O. Gühne, e-print quant-ph/0405165.
  • 67
    • 85015726635 scopus 로고    scopus 로고
    • G. Tóth and O. Gühne, e-print quant-ph/0405165
    • G. Tóth (private communication); see also, V. Scarani, A. Acín, E. Schenck, and M. Aspelmeyer, e-print quant-ph/0405119; G. Tóth and O. Gühne, e-print quant-ph/0405165.
  • 69
    • 1642370829 scopus 로고    scopus 로고
    • P. Hayden, D. W. Leung, P. W. Shor, and A. Winter, e print quant-ph/0307104
    • D. P. DiVincenzo, M. Horodecki, D. W. Leung, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 92, 067902 (2004); P. Hayden, D. W. Leung, P. W. Shor, and A. Winter, e print quant-ph/0307104.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.