메뉴 건너뛰기




Volumn 67, Issue 6, 2003, Pages 623081-6230815

Construction of extremal local positive-operator-valued measures under symmetry

Author keywords

[No Author keywords available]

Indexed keywords

DATA PROCESSING; MATRIX ALGEBRA; PROBABILITY;

EID: 0042510721     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (24)

References (56)
  • 1
    • 0032341219 scopus 로고    scopus 로고
    • M.B. Plenio and V. Vedral, Contemp. Phys. 39, 431 (1998); R. F. Werner, Quantum Information-An Introduction to Basic Theoretical Concepts and Experiments, Springer Tracts in Modern Physics Vol. 173 (Springer, Heidelberg, 2001).
    • (1998) Contemp. Phys. , vol.39 , pp. 431
    • Plenio, M.B.1    Vedral, V.2
  • 7
    • 0042222089 scopus 로고    scopus 로고
    • W. Dür and J.I. Cirac, Quantum Inf. Comput. 2, 240 (2002); J.I. Cirac, W. Dur, B. Kraus, and M. Lewenstein, Phys. Rev. Lett. 86, 544 (2001).
    • (2002) Quantum Inf. Comput. , vol.2 , pp. 240
    • Dür, W.1    Cirac, J.I.2
  • 10
    • 12944306647 scopus 로고    scopus 로고
    • E.M. Rains, Phys. Rev. A 60, 173 (1999); 60, 179 (1999).
    • (1999) Phys. Rev. A , vol.60 , pp. 179
  • 15
    • 4444269235 scopus 로고    scopus 로고
    • V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997); V. Vedral and M.B. Plenio, Phys. Rev. A 57, 1619 (1998); M.B. Plenio, S. Virmani, and P. Papadopoulos, J. Phys. A 33, L193 (2000); W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 2275
    • Vedral, V.1    Plenio, M.B.2    Rippin, M.A.3    Knight, P.L.4
  • 16
    • 0032025985 scopus 로고    scopus 로고
    • V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997); V. Vedral and M.B. Plenio, Phys. Rev. A 57, 1619 (1998); M.B. Plenio, S. Virmani, and P. Papadopoulos, J. Phys. A 33, L193 (2000); W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    • (1998) Phys. Rev. A , vol.57 , pp. 1619
    • Vedral, V.1    Plenio, M.B.2
  • 17
    • 0034625194 scopus 로고    scopus 로고
    • V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997); V. Vedral and M.B. Plenio, Phys. Rev. A 57, 1619 (1998); M.B. Plenio, S. Virmani, and P. Papadopoulos, J. Phys. A 33, L193 (2000); W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    • (2000) J. Phys. A , vol.33
    • Plenio, M.B.1    Virmani, S.2    Papadopoulos, P.3
  • 18
    • 4243684526 scopus 로고    scopus 로고
    • V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997); V. Vedral and M.B. Plenio, Phys. Rev. A 57, 1619 (1998); M.B. Plenio, S. Virmani, and P. Papadopoulos, J. Phys. A 33, L193 (2000); W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 2245
    • Wootters, W.K.1
  • 21
    • 85015766155 scopus 로고    scopus 로고
    • e-print quant-ph/0205089; e-print quant-ph/0210134
    • O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, e-print quant-ph/0205089; e-print quant-ph/0210134; P. Horodecki and A. Ekert, Phys. Rev. Lett. 89, 127902 (2002) ; G.M. D'Ariano, C. Macchiavello, and M.G.A. Paris, e-print quant-ph/0211146; J.M.G. Sancho and S.F. Huelga, Phys. Rev. A 61, 042303 (2000).
    • Gühne, O.1    Hyllus, P.2    Bruss, D.3    Ekert, A.4    Lewenstein, M.5    Macchiavello, C.6    Sanpera, A.7
  • 22
    • 0037120391 scopus 로고    scopus 로고
    • O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, e-print quant-ph/0205089; e-print quant-ph/0210134; P. Horodecki and A. Ekert, Phys. Rev. Lett. 89, 127902 (2002) ; G.M. D'Ariano, C. Macchiavello, and M.G.A. Paris, e-print quant-ph/0211146; J.M.G. Sancho and S.F. Huelga, Phys. Rev. A 61, 042303 (2000).
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 127902
    • Horodecki, P.1    Ekert, A.2
  • 23
    • 85015718301 scopus 로고    scopus 로고
    • e-print quant-ph/0211146
    • O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, e-print quant-ph/0205089; e-print quant-ph/0210134; P. Horodecki and A. Ekert, Phys. Rev. Lett. 89, 127902 (2002) ; G.M. D'Ariano, C. Macchiavello, and M.G.A. Paris, e-print quant-ph/0211146; J.M.G. Sancho and S.F. Huelga, Phys. Rev. A 61, 042303 (2000).
    • D'Ariano, G.M.1    Macchiavello, C.2    Paris, M.G.A.3
  • 24
    • 0347738907 scopus 로고    scopus 로고
    • O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, e-print quant-ph/0205089; e-print quant-ph/0210134; P. Horodecki and A. Ekert, Phys. Rev. Lett. 89, 127902 (2002) ; G.M. D'Ariano, C. Macchiavello, and M.G.A. Paris, e-print quant-ph/0211146; J.M.G. Sancho and S.F. Huelga, Phys. Rev. A 61, 042303 (2000).
    • (2000) Phys. Rev. A , vol.61 , pp. 042303
    • Sancho, J.M.G.1    Huelga, S.F.2
  • 26
    • 0037201580 scopus 로고    scopus 로고
    • J. Walgate and L. Hardy, Phys. Rev. Lett. 89, 147901 (2002); A. Sen De and U. Sen, e-print quant-ph/0203007.
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 147901
    • Walgate, J.1    Hardy, L.2
  • 27
    • 0037201580 scopus 로고    scopus 로고
    • e-print quant-ph/0203007
    • J. Walgate and L. Hardy, Phys. Rev. Lett. 89, 147901 (2002); A. Sen De and U. Sen, e-print quant-ph/0203007.
    • Sen De, A.1    Sen, U.2
  • 28
    • 0035903728 scopus 로고    scopus 로고
    • S. Virmani, M. Sacchi, M.B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 65, 022320 (2002); 64, 064303 (2001); S. Ghosh, G. Kar, A. Roy, D. Sarkar, A. Sen De, and U. Sen, ibid. 65, 062307 (2002); M. Hillery and J. Mimih, e-print quant-ph/0210179.
    • (2001) Phys. Lett. A , vol.288 , pp. 62
    • Virmani, S.1    Sacchi, M.2    Plenio, M.B.3    Markham, D.4
  • 29
    • 4243751569 scopus 로고    scopus 로고
    • S. Virmani, M. Sacchi, M.B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 65, 022320 (2002); 64, 064303 (2001); S. Ghosh, G. Kar, A. Roy, D. Sarkar, A. Sen De, and U. Sen, ibid. 65, 062307 (2002); M. Hillery and J. Mimih, e-print quant-ph/0210179.
    • (2002) Phys. Rev. A , vol.65 , pp. 022320
    • Chen, Y.-X.1    Yang, D.2
  • 30
    • 0035422555 scopus 로고    scopus 로고
    • S. Virmani, M. Sacchi, M.B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 65, 022320 (2002); 64, 064303 (2001); S. Ghosh, G. Kar, A. Roy, D. Sarkar, A. Sen De, and U. Sen, ibid. 65, 062307 (2002); M. Hillery and J. Mimih, e-print quant-ph/0210179.
    • (2001) Phys. Rev. A , vol.64 , pp. 064303
  • 31
    • 0036600157 scopus 로고    scopus 로고
    • S. Virmani, M. Sacchi, M.B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 65, 022320 (2002); 64, 064303 (2001); S. Ghosh, G. Kar, A. Roy, D. Sarkar, A. Sen De, and U. Sen, ibid. 65, 062307 (2002); M. Hillery and J. Mimih, e-print quant-ph/0210179.
    • (2002) Phys. Rev. A , vol.65 , pp. 062307
    • Ghosh, S.1    Kar, G.2    Roy, A.3    Sarkar, D.4    Sen De, A.5    Sen, U.6
  • 32
    • 0035903728 scopus 로고    scopus 로고
    • e-print quant-ph/0210179
    • S. Virmani, M. Sacchi, M.B. Plenio, and D. Markham, Phys. Lett. A 288, 62 (2001); Y.-X. Chen and D. Yang, Phys. Rev. A 65, 022320 (2002); 64, 064303 (2001); S. Ghosh, G. Kar, A. Roy, D. Sarkar, A. Sen De, and U. Sen, ibid. 65, 062307 (2002); M. Hillery and J. Mimih, e-print quant-ph/0210179.
    • Hillery, M.1    Mimih, J.2
  • 36
    • 0036496267 scopus 로고    scopus 로고
    • e-print quant-ph/0210053
    • O.P. DiVincenzo, D.W. Leung, and B.M. Terhal, IEEE Trans. Inf. Theory 48, 580 (2002); D.P. DiVincenzo, P. Hayden, and B.M. Terhal, e-print quant-ph/0210053.
    • Divincenzo, D.P.1    Hayden, P.2    Terhal, B.M.3
  • 45
    • 85015768145 scopus 로고    scopus 로고
    • note
    • i} if it is followed by a local von Neumann measurement by Alice and Bob in the basis {|i}.
  • 48
    • 85015766252 scopus 로고    scopus 로고
    • note
    • μU(U⊗U*)Q(U∈U*)†, where the integral is performed with respect to the Haar measure, U ∈U(d). The analogous operations for the Bell, Werner, and 0 ⊗ 0 symmetries will be referred to as the Bell twirl, Werner twirl, and orthogonal twirl, respectively.
  • 49
    • 0004038786 scopus 로고
    • Omnia Books, Glasgow
    • See entry for the Krein-Milman theorem, in E.J. Borowski and J.M. Borwein, Collins Dictionary of Mathematics (Omnia Books, Glasgow, 1989); for more detail, see R.T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970), Sec. 18.
    • (1989) Collins Dictionary of Mathematics
    • Borowski, E.J.1    Borwein, J.M.2
  • 50
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ, Sec. 18
    • See entry for the Krein-Milman theorem, in E.J. Borowski and J.M. Borwein, Collins Dictionary of Mathematics (Omnia Books, Glasgow, 1989); for more detail, see R.T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970), Sec. 18.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 52
    • 85015784772 scopus 로고    scopus 로고
    • e-print quant-ph/0202121
    • There is at least one other computable separability criterion known to be independent of PPT that also gives homogeneous constraints, namely, the criterion first proposed by Rudolph (O. Rudolph, e-print quant-ph/0202121). Hence the techniques discussed may yield further bounds on LOCC observations using that criterion instead of PPT.
    • Rudolph, O.1
  • 53
    • 85015722813 scopus 로고    scopus 로고
    • note
    • The commutant of a group g of unitaries is defined as the set of all operators A for which [U,A] = 0 for all U ∈ g.
  • 54
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, Theorem 4.3.33
    • R.A. Horn and C.A. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985), Theorem 4.3.33.
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.A.2
  • 55
    • 85015717684 scopus 로고    scopus 로고
    • note
    • A MAPLE 7 script for this task is available by e-mailing a request to s.virmani@ic.ac.uk
  • 56
    • 85015715126 scopus 로고    scopus 로고
    • note
    • T}/d]


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.