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Volumn 44, Issue 4, 2011, Pages

How often is a random quantum state k-entangled?

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EID: 78751604499     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/44/4/045303     Document Type: Article
Times cited : (32)

References (39)
  • 3
    • 31144456196 scopus 로고    scopus 로고
    • On the structure of the body of states with positive partial transpose
    • Szarek S J, Bengtsson I and Žyczkowski K 2006 On the structure of the body of states with positive partial transpose J. Phys. A: Math. Gen. 39 L119-26
    • (2006) J. Phys. A: Math. Gen. , vol.39
    • Szarek, S.J.1    Bengtsson, I.2    Žyczkowski, K.3
  • 4
    • 77953258391 scopus 로고    scopus 로고
    • Approximating the set of separable states using the positive partial transpose test
    • Beigi S and Shor P W 2010 Approximating the set of separable states using the positive partial transpose test J. Math. Phys. 51 042202
    • (2010) J. Math. Phys. , vol.51 , pp. 042202
    • Beigi, S.1    Shor, P.W.2
  • 5
    • 0039624459 scopus 로고
    • Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden variable model
    • Werner R F 1989 Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden variable model Phys. Rev. A 40 4277-81
    • (1989) Phys. Rev. A , vol.40 , pp. 4277-4281
    • Werner, R.F.1
  • 6
    • 0347078542 scopus 로고    scopus 로고
    • A Schmidt number for density matrices
    • Terhal B and Horodecki P 2000 A Schmidt number for density matrices Phys. Rev. A 61 040301
    • (2000) Phys. Rev. A , vol.61 , pp. 040301
    • Terhal, B.1    Horodecki, P.2
  • 9
    • 0036994563 scopus 로고    scopus 로고
    • Largest separable balls around the maximally mixed bipartite quantum state
    • Gurvits L and Barnum H 2002 Largest separable balls around the maximally mixed bipartite quantum state Phys. Rev. A 66 062311
    • (2002) Phys. Rev. A , vol.66 , pp. 062311
    • Gurvits, L.1    Barnum, H.2
  • 10
    • 18244422208 scopus 로고    scopus 로고
    • Separable balls around the maximally mixed multipartite quantum states
    • Gurvits L and Barnum H 2003 Separable balls around the maximally mixed multipartite quantum states Phys. Rev. A 68 042312
    • (2003) Phys. Rev. A , vol.68 , pp. 042312
    • Gurvits, L.1    Barnum, H.2
  • 11
    • 28844465382 scopus 로고    scopus 로고
    • The volume of separable states is super-doubly-exponentially small in the number of qubits
    • Szarek S J 2005 The volume of separable states is super-doubly- exponentially small in the number of qubits Phys. Rev. A 72 032304
    • (2005) Phys. Rev. A , vol.72 , pp. 032304
    • Szarek, S.J.1
  • 12
    • 28844466937 scopus 로고    scopus 로고
    • Better bound on the exponent of the radius of the multipartite separable ball
    • Gurvits L and Barnum H 2005 Better bound on the exponent of the radius of the multipartite separable ball Phys. Rev. A 72 032322
    • (2005) Phys. Rev. A , vol.72 , pp. 032322
    • Gurvits, L.1    Barnum, H.2
  • 13
    • 33144464230 scopus 로고    scopus 로고
    • Tensor products of convex sets and the volume of separable states on N qudits
    • Aubrun G and Szarek S J 2006 Tensor products of convex sets and the volume of separable states on N qudits Phys. Rev. A 73 022109
    • (2006) Phys. Rev. A , vol.73 , pp. 022109
    • Aubrun, G.1    Szarek, S.J.2
  • 14
    • 34547361403 scopus 로고    scopus 로고
    • Entangled states close to the maximally mixed state
    • Hildebrand R 2007 Entangled states close to the maximally mixed state Phys. Rev. A 75 062330
    • (2007) Phys. Rev. A , vol.75 , pp. 062330
    • Hildebrand, R.1
  • 15
    • 0001226716 scopus 로고    scopus 로고
    • Volume of the set of separable states II
    • Žyczkowski K 1999 Volume of the set of separable states II Phys. Rev. A 60 3496-507
    • (1999) Phys. Rev. A , vol.60 , pp. 3496-3507
    • Žyczkowski, K.1
  • 16
    • 8744259975 scopus 로고    scopus 로고
    • Silver mean conjectures for 15-d volumes and 14-d hyperareas of the separable two-qubit systems
    • Slater P B 2005 Silver mean conjectures for 15-d volumes and 14-d hyperareas of the separable two-qubit systems J. Geom. Phys. 53 74-97
    • (2005) J. Geom. Phys. , vol.53 , pp. 74-97
    • Slater, P.B.1
  • 17
    • 69749115934 scopus 로고    scopus 로고
    • On the Bures volume of separable quantum states
    • Ye D 2009 On the Bures volume of separable quantum states J. Math. Phys. 50 083502
    • (2009) J. Math. Phys. , vol.50 , pp. 083502
    • Ye, D.1
  • 18
    • 84887252158 scopus 로고    scopus 로고
    • On the comparison of volumes of quantum states
    • Ye D 2010 On the comparison of volumes of quantum states J. Phys. A: Math. Theor. 43 315301
    • (2010) J. Phys. A: Math. Theor , vol.43 , pp. 315301
    • Ye, D.1
  • 19
    • 0016522050 scopus 로고
    • Completely positive linear maps on complex matrices
    • Choi M D 1975 Completely positive linear maps on complex matrices Linear Algebra Appl. 10 285-90
    • (1975) Linear Algebra Appl. , vol.10 , pp. 285-290
    • Choi, M.D.1
  • 21
    • 67650494727 scopus 로고    scopus 로고
    • Cones of positive maps and their duality relations
    • Skowronek L, Størmer E and Zyczkowski K 2009 Cones of positive maps and their duality relations J. Math. Phys. 50 870-92
    • (2009) J. Math. Phys. , vol.50 , pp. 870-892
    • Skowronek, L.1    Størmer, E.2    Zyczkowski, K.3
  • 22
    • 31244433606 scopus 로고    scopus 로고
    • An analysis of completely-positive trace-preserving maps on 2 × 2 matrices
    • Ruskai M B, Szarek S and Werner E 2002 An analysis of completely-positive trace-preserving maps on 2 × 2 matrices Linear Algebra Appl. 347 159-87
    • (2002) Linear Algebra Appl. , vol.347 , pp. 159-187
    • Ruskai, M.B.1    Szarek, S.2    Werner, E.3
  • 23
    • 3042656008 scopus 로고    scopus 로고
    • On duality between quantum states and quantum maps
    • Zyczkowski K and Bengtsson I 2004 On duality between quantum states and quantum maps Open Syst. Inf. Dyn. 11 3-42
    • (2004) Open Syst. Inf. Dyn , vol.11 , pp. 3-42
    • Zyczkowski, K.1    Bengtsson, I.2
  • 25
    • 37149008020 scopus 로고    scopus 로고
    • The Jamiolkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt numberk and k-positive maps
    • Ranade R S and Ali M 2007 The Jamiolkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt numberk and k-positive maps Open Syst. Inf. Dyn. 14 371-8
    • (2007) Open Syst. Inf. Dyn , vol.14 , pp. 371-378
    • Ranade, R.S.1    Ali, M.2
  • 26
    • 41549151242 scopus 로고    scopus 로고
    • Geometry of sets of quantum maps: A generic positive map acting on a high-dimensional system is not completely positive
    • Szarek S J, Werner E and Życzkowski K 2008 Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive J. Math. Phys. 49 032113
    • (2008) J. Math. Phys. , vol.49 , pp. 032113
    • Szarek, S.J.1    Werner, E.2    Zyczkowski, K.3
  • 27
    • 4544373108 scopus 로고    scopus 로고
    • Statistical properties of random density matrices
    • Sommers H-J and Zyczkowski K 2004 Statistical properties of random density matrices J. Phys. A: Math. Gen. 37 8457-66
    • (2004) J. Phys. A: Math. Gen. , vol.37 , pp. 8457-8466
    • Sommers, H.-J.1    Zyczkowski, K.2
  • 28
    • 18544388060 scopus 로고    scopus 로고
    • Characterization of distillability of entanglement in terms of positive maps
    • Clarisse L 2005 Characterization of distillability of entanglement in terms of positive maps Phys. Rev. A 71 032332
    • (2005) Phys. Rev. A , vol.71 , pp. 032332
    • Clarisse, L.1
  • 31
    • 0000660999 scopus 로고
    • The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
    • Dudley R M 1967 The sizes of compact subsets of Hilbert space and continuity of Gaussian processes J. Funct. Anal. 1 290-330
    • (1967) J. Funct. Anal. , vol.1 , pp. 290-330
    • Dudley, R.M.1
  • 32
    • 0001052429 scopus 로고
    • An affine invariant for convex bodies of n-dimensional space (Spanish)
    • Santaló L A 1949 An affine invariant for convex bodies of n-dimensional space (Spanish) Port. Math. 8 155-61
    • (1949) Port. Math. , vol.8 , pp. 155-161
    • Santaló, L.A.1
  • 34
    • 52449130367 scopus 로고    scopus 로고
    • From the Mahler conjecture to Gauss linking integrals
    • Kuperberg G 2008 From the Mahler conjecture to Gauss linking integrals Geom. Funct. Anal. 18 870-92
    • (2008) Geom. Funct. Anal. , vol.18 , pp. 870-892
    • Kuperberg, G.1
  • 35
    • 0012913015 scopus 로고
    • The finite-dimensional basis problem with an appendix on nets of Grassmann manifolds
    • Szarek S J 1983 The finite-dimensional basis problem with an appendix on nets of Grassmann manifolds Acta Math. 151 153-79
    • (1983) Acta Math. , vol.151 , pp. 153-179
    • Szarek, S.J.1
  • 36
    • 0011697808 scopus 로고
    • Nets of Grassmann manifold and orthogonal groups
    • Iowa City, IO: University of Iowa Press
    • Szarek S J 1982 Nets of Grassmann manifold and orthogonal groups Proc. Banach Space Workshop (Iowa City, IO: University of Iowa Press) pp 169-85
    • (1982) Proc. Banach Space Workshop , pp. 169-185
    • Szarek, S.J.1
  • 37
    • 0039519291 scopus 로고    scopus 로고
    • Metric entropy of homogeneous spaces
    • Warsaw: Polish Academy Sciences
    • Szarek S J 1998 Metric entropy of homogeneous spaces Quantum Probability (Banach Center Publ. vol 43) (Warsaw: Polish Academy Sciences) pp 395-410
    • (1998) Quantum. Probability (Banach Center Publ , vol.43 , pp. 395-410
    • Szarek, S.J.1
  • 38
    • 78049441828 scopus 로고    scopus 로고
    • Schmidt norms for quantum states
    • arXiv:0909.3907v4 quant-ph
    • Johnston N and Kribs D W 2010 Schmidt norms for quantum states J. Math. Phys. 51 082202 (arXiv:0909.3907v4 [quant-ph])
    • (2010) J. Math. Phys. , vol.51 , pp. 082202
    • Johnston, N.1    Kribs, D.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.