메뉴 건너뛰기




Volumn 1, Issue 3, 2012, Pages

The Absolute Positive Partial Transpose Property for Random Induced States

Author keywords

positive partial transpose; PPT criterion; quantum entanglement; random matrices; Separable quantum states; volume induced by partial trace

Indexed keywords


EID: 84868352000     PISSN: 20103263     EISSN: 20103271     Source Type: Journal    
DOI: 10.1142/S2010326312500025     Document Type: Article
Times cited : (20)

References (45)
  • 1
    • 85045572328 scopus 로고    scopus 로고
    • Partial transposition of random states and non-centered semicircular distributions
    • 1250001
    • G. Aubrun, Partial transposition of random states and non-centered semicircular distributions, Random Matrices: Theory Appl. 1(2) (2012), 1250001 (29 pages).
    • (2012) Random Matrices: Theory Appl. , vol.1 , Issue.2 , pp. 29
    • Aubrun, G.1
  • 2
    • 33144464230 scopus 로고    scopus 로고
    • Tensor products of convex sets and the volume of separable states on N qudits
    • G. Aubrun and S. J. Szarek, Tensor products of convex sets and the volume of separable states on N qudits, Phys. Rev. A 73 (2006) 022109.
    • (2006) Phys Rev. A , vol.73 , pp. 022109
    • Aubrun, G.1    Szarek, S.J.2
  • 3
    • 79956161226 scopus 로고    scopus 로고
    • Hastings' additivity counterexample via Dvoretzky's theorem
    • G. Aubrun, S. Szarek and E.Werner, Hastings' additivity counterexample via Dvoretzky's theorem, Comm. Math. Phys. 305 (2011) 85-97.
    • (2011) Comm. Math. Phys. , vol.305 , pp. 85-97
    • Aubrun, G.1    Szarek, S.2    Werner, E.3
  • 5
    • 84858395661 scopus 로고    scopus 로고
    • Phase transitions for random states and a semi-circle law for the partial transpose
    • 4 pages
    • G. Aubrun, S. Szarek and D. Ye, Phase transitions for random states and a semi-circle law for the partial transpose, Phy. Rev. A. 85 (2012) 030302(R) (4 pages).
    • (2012) Phy. Rev. A. , vol.85 , pp. 30302
    • Aubrun, G.1    Szarek, S.2    Ye, D.3
  • 7
    • 0011324907 scopus 로고
    • Convergence to the semicircle law
    • Z. D. Bai and Y. Q. Yin, Convergence to the semicircle law, Ann. Probab. 16 (1988) 863-875.
    • (1988) Ann Probab. , vol.16 , pp. 863-875
    • Bai, Z.D.1    Yin, Y.Q.2
  • 8
    • 0002964353 scopus 로고    scopus 로고
    • Some properties of crossings and partitions
    • P. Biane, Some properties of crossings and partitions, Discrete Math. 175 (1997) 41-53.
    • (1997) Discrete Math. , vol.175 , pp. 41-53
    • Biane, P.1
  • 9
    • 0032207908 scopus 로고    scopus 로고
    • Strong asymptotics for Laguerre polynomials with varying weights
    • C. Bosbach and W. Gawronski, Strong asymptotics for Laguerre polynomials with varying weights, J. Comput. Appl. Math. 99 (1998) 77-89.
    • (1998) J. Comput. Appl. Math. , vol.99 , pp. 77-89
    • Bosbach, C.1    Gawronski, W.2
  • 10
    • 85080912567 scopus 로고    scopus 로고
    • online first
    • T. Banica and I. Nechita, Asymptotic eigenvalue distributions of block-transposed Wishart matrices, arXiv:1105.2556. J. Theore. Probab, online first.
    • J. Theore. Probab
    • Banica, T.1    Nechita, I.2
  • 12
    • 79958209718 scopus 로고    scopus 로고
    • Gaussianization and eigenvalue statistics for random quantum channels (III)
    • B. Collins and I. Nechita, Gaussianization and eigenvalue statistics for random quantum channels (III), Ann. Appl. Probab. 21 (2011) 1136-1179.
    • (2011) Ann. Appl. Probab. , vol.21 , pp. 1136-1179
    • Collins, B.1    Nechita, I.2
  • 13
    • 33947385649 scopus 로고
    • Can quantum-mechanical description of physical reality be considered complete
    • A. Einstein, B. Podolsky and N. Rosen, Can quantum-mechanical description of physical reality be considered complete Phys. Rev. 47 (1935) 777-780.
    • (1935) Phys Rev. , vol.47 , pp. 777-780
    • Einstein, A.1    Podolsky, B.2    Rosen, N.3
  • 15
    • 79959705851 scopus 로고    scopus 로고
    • From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking
    • [quant-ph]
    • O. Fawzi, P. Hayden and P. Sen, From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking, in Proceedings of 43rd ACM STOC (2011), arXiv:1010.3007v3 [quant-ph].
    • (2011) Proceedings of 43rd ACM STOC
    • Fawzi, O.1    Hayden, P.2    Sen, P.3
  • 16
    • 0041345998 scopus 로고    scopus 로고
    • Classical deterministic complexity of Edmond's problem and quantum entanglement
    • ACM, New York, (Electronic)
    • L. Gurvits, Classical deterministic complexity of Edmond's problem and quantum entanglement, Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (ACM, New York, 2003), pp. 10-19 (Electronic).
    • (2003) Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing , pp. 10-19
    • Gurvits, L.1
  • 17
    • 0036994563 scopus 로고    scopus 로고
    • Largest separable balls around the maximally mixed bipartite quantum state
    • L. Gurvits and H. Barnum, Largest separable balls around the maximally mixed bipartite quantum state, Phys. Rev. A 66 (2002) 062311.
    • (2002) Phys. Rev. A , vol.66 , pp. 062311
    • Gurvits, L.1    Barnum, H.2
  • 18
    • 63849119968 scopus 로고    scopus 로고
    • Superadditivity of communication capacity using entangled inputs
    • M. B. Hastings, Superadditivity of communication capacity using entangled inputs, Nat. Phys. 5 (2009) 255-257.
    • (2009) Nat. Phys. , vol.5 , pp. 255-257
    • Hastings, M.B.1
  • 20
    • 36549079515 scopus 로고    scopus 로고
    • Positive partial transpose from spectra
    • R. Hildebrand, Positive partial transpose from spectra, Phys. Rev. A 76 (2007) 052325.
    • (2007) Phys. Rev. A , vol.76 , pp. 052325
    • Hildebrand, R.1
  • 22
    • 0042376719 scopus 로고    scopus 로고
    • Separability of mixed states: Necessary and sufficient conditions
    • M. Horodecki, P. Horodecki and R. Horodecki, Separability of mixed states: Necessary and sufficient conditions, Phys. Lett. A 223 (1996) 1-8.
    • (1996) Phys. Lett. A , vol.223 , pp. 1-8
    • Horodecki, M.1    Horodecki, P.2    Horodecki, R.3
  • 23
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29 (2001) 295-327.
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.1
  • 24
    • 78651341854 scopus 로고    scopus 로고
    • Large deviations of the smallest eigenvalue of the Wishart-Laguerre ensemble
    • E. Katzav and I. P. Castillo, Large deviations of the smallest eigenvalue of the Wishart-Laguerre ensemble, Phys. Rev. E 82 (2010) 040104(R).
    • (2010) Phys Rev. E , vol.82 , pp. 40104
    • Katzav, E.1    Castillo, I.P.2
  • 25
    • 0035279037 scopus 로고    scopus 로고
    • Geometry of entangled states
    • 3
    • M. Kús and K. Z yczkowski, Geometry of entangled states, Phys. Rev. A (3) 63(3) (2001) 032307.
    • (2001) Phys. Rev. A , vol.3 , Issue.63 , pp. 032307
    • Kús, M.1    Zyczkowski, K.2
  • 26
    • 39049092375 scopus 로고    scopus 로고
    • Asymptotics of random density matrices
    • I. Nechita, Asymptotics of random density matrices, Ann. Henri Poincaré 8 (2007) 1521-1538.
    • (2007) Ann. Henri Poincaré , vol.8 , pp. 1521-1538
    • Nechita, I.1
  • 31
    • 0037574296 scopus 로고    scopus 로고
    • Separability criterion for density matrices
    • A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77 (1996) 1413-1415.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 1413-1415
    • Peres, A.1
  • 32
    • 84963019102 scopus 로고
    • Convex bodies associated with a given convex body
    • C. A. Rogers and G. C. Shephard, Convex bodies associated with a given convex body, J. London Math. Soc. 33 (1958) 270-281.
    • (1958) J London Math. Soc. , vol.33 , pp. 270-281
    • Rogers, C.A.1    Shephard, G.C.2
  • 33
    • 85115374351 scopus 로고
    • Algorithms for quantum computation: Discrete logarithms and factoring
    • P. W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in IEEE Symposium on Foundations of Computer Science (1994), pp. 124-134.
    • (1994) IEEE Symposium on Foundations of Computer Science , pp. 124-134
    • Shor, P.W.1
  • 34
    • 0141450345 scopus 로고    scopus 로고
    • A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
    • A. Soshnikov, A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices, J. Statist. Phys. 108 (2002) 1033-1056.
    • (2002) J. Statist. Phys. , vol.108 , pp. 1033-1056
    • Soshnikov, A.1
  • 35
    • 0000896652 scopus 로고
    • Positive linear maps of operator algebras
    • E. Stormer, Positive linear maps of operator algebras, Acta Math. 110 (1963) 233-278.
    • (1963) Acta Math. , vol.110 , pp. 233-278
    • Stormer, E.1
  • 36
    • 28844465382 scopus 로고    scopus 로고
    • The volume of separable states is super-doubly-exponentially small in the number of qubits
    • S. J. Szarek, The volume of separable states is super-doubly-exponentially small in the number of qubits, Phys. Rev. A 72 (2005) 032304.
    • (2005) Phys. Rev. A , vol.72 , pp. 032304
    • Szarek, S.J.1
  • 37
    • 31144456196 scopus 로고    scopus 로고
    • On the structure of the body of states with positive partial transpose
    • S. J. Szarek, I. Bengtsson and K. Z yczkowski, On the structure of the body of states with positive partial transpose, J. Phys. A: Math. Gen. 39 (2006) L119-L126.
    • (2006) J. Phys. A: Math. Gen. , vol.39 , pp. L119-L126
    • Szarek, S.J.1    Bengtsson, I.2    Zyczkowski, K.3
  • 38
    • 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
    • S. Szarek, E. Werner and K. Zyczkowski, Geometry of sets of quantum maps: A generic positive map acting on a high-dimensional system is not completely positive, J. Math. Phys. 49 (2008) 032113.
    • (2008) J. Math. Phys. , vol.49 , pp. 032113
    • Szarek, S.1    Werner, E.2    Zyczkowski, K.3
  • 40
    • 0039624459 scopus 로고
    • Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
    • R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40 (1989) 4277-4281.
    • (1989) Phys. Rev. A , vol.40 , pp. 4277-4281
    • Werner, R.F.1
  • 41
    • 0000260392 scopus 로고
    • Positive maps of low dimensional matrix algebra
    • S. L. Woronowicz, Positive maps of low dimensional matrix algebra, Rep. Math. Phys. 10 (1976) 165-183.
    • (1976) Rep. Math. Phys. , vol.10 , pp. 165-183
    • Woronowicz, S.L.1
  • 42
    • 69749115934 scopus 로고    scopus 로고
    • On the Bures volume of separable quantum states
    • D. Ye, On the Bures volume of separable quantum states, J. Math. Phy. 50 (2009) 083502.
    • (2009) J. Math. Phy. , vol.50 , pp. 083502
    • Ye, D.1
  • 43
    • 84887252158 scopus 로고    scopus 로고
    • On the comparison of volumes of quantum states
    • (17 pages)
    • D. Ye, On the comparison of volumes of quantum states, J. Phys. A: Math. Theor. 43 (2010) 315301 (17 pages).
    • (2010) J. Phys. A: Math. Theor. , vol.43 , pp. 315301
    • Ye, D.1
  • 44
    • 0031258947 scopus 로고    scopus 로고
    • Matrix integrals and map enumeration: An accessible introduction
    • Combinatorics and physics (Marseilles, 1995)
    • A. Zvonkin, Matrix integrals and map enumeration: An accessible introduction, Math. Comput. Modell. 26(8-10) (1997) 281-304. Combinatorics and physics (Marseilles, 1995).
    • (1997) Math. Comput. Modell. , vol.26 , Issue.8-10 , pp. 281-304
    • Zvonkin, A.1
  • 45
    • 0035823453 scopus 로고    scopus 로고
    • Induced measures in the space of mixed quantum states
    • K. Z yczkowski and H.-J. Sommers, Induced measures in the space of mixed quantum states, J. Phys. A 34 (2001) 7111.
    • (2001) J. Phys. A , vol.34 , pp. 7111
    • Zyczkowski, K.1    Sommers, H.-J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.