메뉴 건너뛰기




Volumn 7, Issue 3, 2007, Pages 209-227

Convex hulls of varieties and entanglement measures based on the roof construction

Author keywords

Algebraic geometry; Entanglement measures

Indexed keywords

ALGEBRA; COMPUTATIONAL GEOMETRY; DECOMPOSITION; OPTICAL VARIABLES CONTROL; ROOFS;

EID: 34247253919     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (14)

References (32)
  • 1
    • 85115374351 scopus 로고
    • Algorithms for quantum computation: Discrete logarithms and factoring
    • IEEE Comput. Soc. Press, Los Alamitos, CA
    • Peter W. Shor. Algorithms for quantum computation: discrete logarithms and factoring. In 35th Annual Symposium on Foundations of Computer Science (Santa Fe, NM, 1994), pages 124-134. IEEE Comput. Soc. Press, Los Alamitos, CA, 1994.
    • (1994) 35th Annual Symposium on Foundations of Computer Science (Santa Fe, NM, 1994) , pp. 124-134
    • Shor, P.W.1
  • 2
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput., 26(5):1484-1509, 1997.
    • (1997) SIAM J. Comput , vol.26 , Issue.5 , pp. 1484-1509
    • Shor, P.W.1
  • 3
    • 4243059985 scopus 로고
    • Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels
    • Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels. Phys. Rev. Lett., 70(13):1895-1899, 1993.
    • (1993) Phys. Rev. Lett , vol.70 , Issue.13 , pp. 1895-1899
    • Bennett, C.H.1    Brassard, G.2    Crépeau, C.3    Jozsa, R.4    Peres, A.5    Wootters, W.K.6
  • 5
    • 0000260392 scopus 로고
    • Positive maps of low dimensional matrix algebras
    • S. L. Woronowicz. Positive maps of low dimensional matrix algebras. Rep. Math. Phys., 10(2):165-183, 1976.
    • (1976) Rep. Math. Phys , vol.10 , Issue.2 , pp. 165-183
    • Woronowicz, S.L.1
  • 6
    • 0042542909 scopus 로고    scopus 로고
    • Separability criterion and inseparable mixed states with positive partial transposition
    • Pawel Horodecki. Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A, 232(5):333-339, 1997.
    • (1997) Phys. Lett. A , vol.232 , Issue.5 , pp. 333-339
    • Horodecki, P.1
  • 7
    • 0346488842 scopus 로고    scopus 로고
    • Distillation and bound entanglement
    • Paweł Horodecki and Ryszard Horodecki. Distillation and bound entanglement. Quantum Inf. Comput., 1(1):45-75, 2001.
    • (2001) Quantum Inf. Comput , vol.1 , Issue.1 , pp. 45-75
    • Horodecki, P.1    Horodecki, R.2
  • 8
    • 0035584893 scopus 로고    scopus 로고
    • A family of indecomposable positive linear maps based on entangled quantum states
    • Barbara M. Terhal. A family of indecomposable positive linear maps based on entangled quantum states. Linear Algebra Appl., 323(1-3):61-73, 2001.
    • (2001) Linear Algebra Appl , vol.323 , Issue.1-3 , pp. 61-73
    • Terhal, B.M.1
  • 9
    • 4644359625 scopus 로고    scopus 로고
    • Entanglement of a Pair of Quantum Bits
    • Scott Hill and William K. Wootters. Entanglement of a Pair of Quantum Bits. Phys. Rev. Lett., 78(26):5022-5025, 1997.
    • (1997) Phys. Rev. Lett , vol.78 , Issue.26 , pp. 5022-5025
    • Hill, S.1    Wootters, W.K.2
  • 10
    • 4243684526 scopus 로고    scopus 로고
    • Entanglement of Formation of an Arbitrary State of Two Qubits
    • William K. Wootters. Entanglement of Formation of an Arbitrary State of Two Qubits. Phys. Rev. Lett., 80(10):2245-2248, 1998.
    • (1998) Phys. Rev. Lett , vol.80 , Issue.10 , pp. 2245-2248
    • Wootters, W.K.1
  • 11
    • 0034271951 scopus 로고    scopus 로고
    • Fidelity and concurrence of conjugated states
    • Armin Uhlmann. Fidelity and concurrence of conjugated states. Phys. Rev. A, 62(3):032307, 2000.
    • (2000) Phys. Rev. A , vol.62 , Issue.3 , pp. 032307
    • Uhlmann, A.1
  • 12
    • 0035505193 scopus 로고    scopus 로고
    • Variational characterizations of separability and entanglement of formation
    • Koenraad Audenaert, Frank Verstraete, and Bart De Moor. Variational characterizations of separability and entanglement of formation. Phys. Rev. A, 64(5):052304, 2001.
    • (2001) Phys. Rev. A , vol.64 , Issue.5 , pp. 052304
    • Audenaert, K.1    Verstraete, F.2    Moor, B.D.3
  • 14
    • 0003908675 scopus 로고    scopus 로고
    • Ideals, varieties, and algorithms
    • Springer-Verlag, New York, 2nd edition
    • David Cox, John Little, and Donal O'Shea. Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2nd edition, 1997.
    • (1997) Undergraduate Texts in Mathematics
    • Cox, D.1    Little, J.2    O'Shea, D.3
  • 15
    • 4444312484 scopus 로고
    • Algebraic geometry
    • of, Springer-Verlag, New York
    • Joe Harris. Algebraic geometry, volume 133 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995.
    • (1995) Graduate Texts in Mathematics , vol.133
    • Harris, J.1
  • 16
    • 0003322387 scopus 로고
    • Algebraic geometry
    • of, Springer-Verlag, New York
    • Robin Hartshorne. Algebraic geometry, volume 52 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1977.
    • (1977) Graduate Texts in Mathematics , vol.52
    • Hartshorne, R.1
  • 18
    • 0000179033 scopus 로고    scopus 로고
    • Entropy and optimal decompositions of states relative to a maximal commutative subalgebra
    • Armin Uhlmann. Entropy and optimal decompositions of states relative to a maximal commutative subalgebra. Open Syst. Inf. Dyn., 5(3):209-228, 1998.
    • (1998) Open Syst. Inf. Dyn , vol.5 , Issue.3 , pp. 209-228
    • Uhlmann, A.1
  • 20
    • 0003352688 scopus 로고    scopus 로고
    • Using algebraic geometry
    • of, Springer-Verlag, New York
    • David Cox, John Little, and Donal O'Shea. Using algebraic geometry, volume 185 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1998.
    • (1998) Graduate Texts in Mathematics , vol.185
    • Cox, D.1    Little, J.2    O'Shea, D.3
  • 21
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge
    • Roger A. Horn and Charles R. Johnson. Matrix analysis. Cambridge University Press, Cambridge, 1990.
    • (1990) Matrix analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 22
    • 0030636914 scopus 로고    scopus 로고
    • Geometric Phases for SU(3) Representations and Three Level Quantum Systems
    • G. Khanna, S. Mukhopadhyay, R. Simon, and N. Mukunda. Geometric Phases for SU(3) Representations and Three Level Quantum Systems. Ann. Physics, 253(1):55-82, 1997.
    • (1997) Ann. Physics , vol.253 , Issue.1 , pp. 55-82
    • Khanna, G.1    Mukhopadhyay, S.2    Simon, R.3    Mukunda, N.4
  • 23
    • 0031557514 scopus 로고    scopus 로고
    • A generalized Pancharatnam geometric phase formula for three-level quantum systems
    • Arvind, K. S. Mallesh, and N. Mukunda. A generalized Pancharatnam geometric phase formula for three-level quantum systems. J. Phys. A, 30(7):2417-2431, 1997.
    • (1997) J. Phys. A , vol.30 , Issue.7 , pp. 2417-2431
    • Arvind, K.1    Mallesh, S.2    Mukunda, N.3
  • 24
    • 34247206207 scopus 로고    scopus 로고
    • John Preskill. Physics 229: Advanced Mathematical Methods of Physics - Quantum Computation and Information. California Institute of Technology, http://www.theory.caltech/edu/people/preskill/ph229/, 1998.
    • John Preskill. Physics 229: Advanced Mathematical Methods of Physics - Quantum Computation and Information. California Institute of Technology, http://www.theory.caltech/edu/people/preskill/ph229/, 1998.
  • 26
    • 84927006707 scopus 로고
    • Probability relations between separated systems
    • E. Schrödinger. Probability relations between separated systems. Proc. Camb. Philos. Soc., 32:446-452, 1936.
    • (1936) Proc. Camb. Philos. Soc , vol.32 , pp. 446-452
    • Schrödinger, E.1
  • 27
    • 11944275853 scopus 로고
    • Information theory and statistical mechanics. II
    • E. T. Jaynes. Information theory and statistical mechanics. II. Phys. Rev., 108(2):171-190, 1957.
    • (1957) Phys. Rev , vol.108 , Issue.2 , pp. 171-190
    • Jaynes, E.T.1
  • 28
    • 0001992982 scopus 로고
    • A complete classification of quantum ensembles having a given density matrix
    • Lane P. Hughston, Richard Jozsa, and William K. Wootters. A complete classification of quantum ensembles having a given density matrix. Phys. Lett. A, 183(1):14-18, 1993.
    • (1993) Phys. Lett. A , vol.183 , Issue.1 , pp. 14-18
    • Hughston, L.P.1    Jozsa, R.2    Wootters, W.K.3
  • 29
    • 4243216277 scopus 로고    scopus 로고
    • Mixed-state entanglement and quantum error correction
    • Charles H. Bennett, David P. DiVincenzo, John A. Smolin, and William K. Wootters. Mixed-state entanglement and quantum error correction. Phys. Rev. A, 54(5):3824-3851, 1996.
    • (1996) Phys. Rev. A , vol.54 , Issue.5 , pp. 3824-3851
    • Bennett, C.H.1    DiVincenzo, D.P.2    Smolin, J.A.3    Wootters, W.K.4
  • 30
    • 0343448353 scopus 로고    scopus 로고
    • Thermodynamics and the measure of entanglement
    • Sandu Popescu and Daniel Rohrlich. Thermodynamics and the measure of entanglement. Phys. Rev. A, 56(5):R3319-R3321, 1997.
    • (1997) Phys. Rev. A , vol.56 , Issue.5
    • Popescu, S.1    Rohrlich, D.2
  • 31
    • 0034652055 scopus 로고    scopus 로고
    • Entanglement monotones
    • Guifré Vidal. Entanglement monotones. J. Mod. Opt., 47(2-3):355-376, 2000.
    • (2000) J. Mod. Opt , vol.47 , Issue.2-3 , pp. 355-376
    • Vidal, G.1
  • 32
    • 0343889804 scopus 로고    scopus 로고
    • Continuity bounds for entanglement
    • M. A. Nielsen. Continuity bounds for entanglement. Phys. Rev. A, 61(6):064301, 2000.
    • (2000) Phys. Rev. A , vol.61 , Issue.6 , pp. 064301
    • Nielsen, M.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.