메뉴 건너뛰기




Volumn 81, Issue 6, 2010, Pages

Probabilistic theories with purification

Author keywords

[No Author keywords available]

Indexed keywords

BIPARTITE STATE; BIT COMMITMENT; MATHEMATICAL FRAMEWORKS; MIXED STATE; PHYSICAL PROCESS; PROBABILISTIC THEORY; PURE STATE; REVERSIBLE INTERACTIONS;

EID: 77954196305     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.062348     Document Type: Article
Times cited : (565)

References (71)
  • 1
    • 21344488159 scopus 로고
    • FNDPA4 0015-9018 10.1007/BF02058098
    • S. Popescu and D. Rohrlich, Found. Phys. FNDPA4 0015-9018 10.1007/BF02058098 24, 379 (1994).
    • (1994) Found. Phys. , vol.24 , pp. 379
    • Popescu, S.1    Rohrlich, D.2
  • 2
    • 28844483860 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.95.140401
    • J. Barrett and S. Pironio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.140401 95, 140401 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 140401
    • Barrett, J.1    Pironio, S.2
  • 3
    • 27144477301 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.95.010503
    • J. Barrett, L. Hardy, and A. Kent, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010503 95, 010503 (2005).
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 010503
    • Barrett, J.1    Hardy, L.2    Kent, A.3
  • 4
    • 33748942504 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.97.120405
    • A. Acín, N. Gisin, and Ll. Masanes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.120405 97, 120405 (2006).
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 120405
    • Acín, A.1    Gisin, N.2    Masanes, Ll.3
  • 5
    • 71449102540 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.103.230403
    • M. M. Wolf, D. Perez-Garcia, and C. Fernandez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.230403 103, 230403 (2009).
    • (2009) Phys. Rev. Lett. , vol.103 , pp. 230403
    • Wolf, M.M.1    Perez-Garcia, D.2    Fernandez, C.3
  • 6
    • 33144457111 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.73.012112
    • Ll. Masanes, A. Acín, and N. Gisin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012112 73, 012112 (2006).
    • (2006) Phys. Rev. A , vol.73 , pp. 012112
    • Masanes, Ll.1    Acín, A.2    Gisin, N.3
  • 8
    • 33847706141 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.75.032304
    • J. Barrett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032304 75, 032304 (2007).
    • (2007) Phys. Rev. A , vol.75 , pp. 032304
    • Barrett, J.1
  • 9
    • 33144456316 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.73.012101
    • A. J. Short, S. Popescu, and N. Gisin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012101 73, 012101 (2006)
    • (2006) Phys. Rev. A , vol.73 , pp. 012101
    • Short, A.J.1    Popescu, S.2    Gisin, N.3
  • 10
    • 77954185085 scopus 로고    scopus 로고
    • H. Barnum, J. Barrett, M. Leifer, and A. Wilce, e-print arXiv: 0805.3553
    • H. Barnum, J. Barrett, M. Leifer, and A. Wilce, e-print arXiv: 0805.3553.
  • 12
    • 0000194417 scopus 로고
    • ANMAAH 0003-486X 10.2307/1968621
    • G. Birkhoff and J. von Neumann, Ann. Math. ANMAAH 0003-486X 10.2307/1968621 37, 823 (1936).
    • (1936) Ann. Math. , vol.37 , pp. 823
    • Birkhoff, G.1    Von Neumann, J.2
  • 16
    • 0008688936 scopus 로고
    • CMPHAY 0010-3616 10.1007/BF01654027
    • G. Ludwig, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01654027 9, 1 (1968);
    • (1968) Commun. Math. Phys. , vol.9 , pp. 1
    • Ludwig, G.1
  • 19
    • 77954181007 scopus 로고    scopus 로고
    • L. Hardy, e-print arXiv: quant-ph/0101012
    • L. Hardy, e-print arXiv: quant-ph/0101012.
  • 20
    • 84926125365 scopus 로고    scopus 로고
    • to appear in edited by A. Bokulich and G. Jaeger (Cambridge University Press, Cambridge, UK
    • G. M. D'Ariano, to appear in Philosophy of Quantum Information and Entanglement, edited by, A. Bokulich, and, G. Jaeger, (Cambridge University Press, Cambridge, UK, 2010).
    • (2010) Philosophy of Quantum Information and Entanglement
    • D'Ariano, G.M.1
  • 21
    • 33751250160 scopus 로고    scopus 로고
    • APCPCS 0094-243X 10.1063/1.2158715
    • G. M. D'Ariano, AIP Conf. Proc. APCPCS 0094-243X 10.1063/1.2158715 810, 114 (2006).
    • (2006) AIP Conf. Proc. , vol.810 , pp. 114
    • D'Ariano, G.M.1
  • 23
    • 44949283969 scopus 로고
    • ADMTA4 0001-8708 10.1016/0001-8708(91)90003-P
    • A. Joyal and R. Street, Adv. Math. ADMTA4 0001-8708 10.1016/0001-8708(91) 90003-P 88, 55 (1991).
    • (1991) Adv. Math. , vol.88 , pp. 55
    • Joyal, A.1    Street, R.2
  • 24
    • 77954204164 scopus 로고    scopus 로고
    • A Survey of Graphical Languages for Monoidal Categories, available at
    • P. Selinger, A Survey of Graphical Languages for Monoidal Categories, available at [http://www.mathstat.dal.ca/selinger/papers/graphical.pdf].
    • Selinger, P.1
  • 27
    • 77954199260 scopus 로고    scopus 로고
    • note
    • In other words, we need to put a probabilistic structure on top of the formal language of circuits. This rule would be given by a function π from T (I, I) to the interval [0, 1], enjoying the properties - i X π (p i) = 1, and π (p i - q j) = π (p i - q j) = π (p i) π (q j). In this presentation, however, we will omit the function π, and we will directly identify the event p i with its probability π (p i).
  • 29
    • 77954193765 scopus 로고    scopus 로고
    • note
    • Note that the extension by linearity C k (- i c i ρ i): = - i c i C k | ρ i) A is well defined: Indeed, one has - i c i ρ i = 0 if and only if - i c i (a | ρ i) A = 0 for every effect a S (A). Now, if b is an arbitrary effect in E (B), then (b | B C k is an effect in E (A), and, therefore, one must have - i c i (b | B C | ρ i) = 0. Since b is arbitrary, this implies - i c i C k | ρ i) = 0, thus proving that the linear extension is well defined.
  • 30
    • 34250495765 scopus 로고
    • CMPHAY 0010-3616 10.1007/BF01647093
    • E. B. Davies and J. T. Lewis, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01647093 17, 239 (1970).
    • (1970) Commun. Math. Phys. , vol.17 , pp. 239
    • Davies, E.B.1    Lewis, J.T.2
  • 31
    • 33947611133 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.75.032110
    • R. W. Spekkens, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032110 75, 032110 (2007).
    • (2007) Phys. Rev. A , vol.75 , pp. 032110
    • Spekkens, R.W.1
  • 32
    • 77954190059 scopus 로고    scopus 로고
    • note
    • - k ≥ 1 - ε / 2. If for every k we associate the outcome 0 to the first m k strings, and the outcome 1 to the remaining ones, this procedure defines a new coin with bias p N = - k p k p (m k | k) satisfying the bound | p - p N | ≤ ε.
  • 33
    • 69549099176 scopus 로고    scopus 로고
    • PLRAAN 1751-8113 10.1088/1751-8113/40/12/S12
    • L. Hardy, J. Phys. A PLRAAN 1751-8113 10.1088/1751-8113/40/12/S12 40, 3081 (2007).
    • (2007) J. Phys. A , vol.40 , pp. 3081
    • Hardy, L.1
  • 34
    • 69549132610 scopus 로고    scopus 로고
    • EULEEJ 0295-5075 10.1209/0295-5075/83/30004
    • G. Chiribella, G. M. D'Ariano, and P. Perinotti, EPL EULEEJ 0295-5075 10.1209/0295-5075/83/30004 83, 30004 (2008).
    • (2008) EPL , vol.83 , pp. 30004
    • Chiribella, G.1    D'Ariano, G.M.2    Perinotti, P.3
  • 35
  • 39
    • 84927006707 scopus 로고
    • MPCPCO 0305-0041 10.1017/S0305004100019137
    • E. Schrödinger, Proc. Cambr. Philos. Soc. MPCPCO 0305-0041 10.1017/S0305004100019137 32, 446 (1936).
    • (1936) Proc. Cambr. Philos. Soc. , vol.32 , pp. 446
    • Schrödinger, E.1
  • 40
    • 77954193020 scopus 로고    scopus 로고
    • H. Barnum, C. P. Gaebler, and A. Wilce, e-print arXiv: 0912.5532
    • H. Barnum, C. P. Gaebler, and A. Wilce, e-print arXiv: 0912.5532.
  • 43
    • 77954183244 scopus 로고    scopus 로고
    • note
    • The general version Choi-Jamiołkowski isomorphism considered in this article is an isomorphism between transformations and bipartite states. This is not the same as the mathematical "CJ isomorphism" of Ref. [18], which was instead the isomorphism between the cone of transformations T + (A, A) and the cone of positive bilinear forms on the complex vector space E C (A) = Span C { E (A) }.
  • 45
    • 84968466834 scopus 로고
    • PAMYAR 0002-9939 10.2307/2032342
    • W. F. Stinespring, Proc. Am. Math. Soc. PAMYAR 0002-9939 10.2307/2032342 6, 211 (1955).
    • (1955) Proc. Am. Math. Soc. , vol.6 , pp. 211
    • Stinespring, W.F.1
  • 47
    • 0001782596 scopus 로고
    • JMAPAQ 0022-2488 10.1063/1.526000
    • M. Ozawa, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.526000 25, 79 (1984).
    • (1984) J. Math. Phys. , vol.25 , pp. 79
    • Ozawa, M.1
  • 48
    • 17744393885 scopus 로고    scopus 로고
    • CMPHAY 0010-3616 10.1007/s00220-005-1317-6
    • I. Devetak and P. Shor, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-005-1317-6 256, 287 (2005).
    • (2005) Commun. Math. Phys. , vol.256 , pp. 287
    • Devetak, I.1    Shor, P.2
  • 51
    • 0016522050 scopus 로고
    • LAAPAW 0024-3795 10.1016/0024-3795(75)90075-0
    • M.-D. Choi, Lin. Alg. Appl. LAAPAW 0024-3795 10.1016/0024-3795(75)90075-0 10, 285 (1975).
    • (1975) Lin. Alg. Appl. , vol.10 , pp. 285
    • Choi, M.-D.1
  • 52
    • 35448975107 scopus 로고
    • RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0
    • A. Jamiołkowski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0 3, 275 (1972).
    • (1972) Rep. Math. Phys. , vol.3 , pp. 275
    • Jamiołkowski, A.1
  • 53
    • 77954211963 scopus 로고    scopus 로고
    • note
    • Indeed, one can immediately see that if two sequences of channels { C m } and { D n } converge to two channels C and D, respectively, then the sequence { C n D n } converges to C D: - C n D n - C D - A, A ≤ - (C n - C) D n - A, A + - C (D n - D) - A, A ≤ - C n - C - A, A + - D n - D - A, A → n → 0, having used the triangle inequality and the monotonicity property of Lemma 9.
  • 56
    • 6844242534 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.54.2614
    • B. Schumacher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.2614 54, 2614 (1996).
    • (1996) Phys. Rev. A , vol.54 , pp. 2614
    • Schumacher, B.1
  • 57
    • 5544295273 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.54.2629
    • B. Schumacher and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.2629 54, 2629 (1996).
    • (1996) Phys. Rev. A , vol.54 , pp. 2629
    • Schumacher, B.1    Nielsen, M.A.2
  • 58
    • 0032099694 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.57.4153
    • H. Barnum, M. A. Nielsen, and B. Schumacher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.4153 57, 4153 (1998).
    • (1998) Phys. Rev. A , vol.57 , pp. 4153
    • Barnum, H.1    Nielsen, M.A.2    Schumacher, B.3
  • 59
    • 53349097453 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.78.032330
    • D. Kretschmann, D. W. Kribs, and R. W. Spekkens, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.032330 78, 032330 (2008).
    • (2008) Phys. Rev. A , vol.78 , pp. 032330
    • Kretschmann, D.1    Kribs, D.W.2    Spekkens, R.W.3
  • 60
    • 0242723800 scopus 로고    scopus 로고
    • JMOPEW 0950-0340 10.1080/09500340308234541
    • M. Gregoratti and R. F. Werner, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340308234541 50, 915 (2003).
    • (2003) J. Mod. Opt. , vol.50 , pp. 915
    • Gregoratti, M.1    Werner, R.F.2
  • 64
    • 33244456370 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.72.062323
    • D. Kretschmann and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062323 72, 062323 (2005).
    • (2005) Phys. Rev. A , vol.72 , pp. 062323
    • Kretschmann, D.1    Werner, R.F.2
  • 66
    • 77954185972 scopus 로고    scopus 로고
    • note
    • For bipartite channels the term "semicausal" was used to mean "allowing for signaling in one direction at most," while the term "causal" was used to mean "not allowing for signaling (in any direction)." For an N -partite channel, however, there are N ! possible orderings of the input systems, and a causal N -partite channel was then defined as a channel that is "allowing for the propagation of signals along one of these possible orderings." Of course, for N = 2 the two nomenclatures conflict.
  • 68
    • 77954179923 scopus 로고    scopus 로고
    • G. Chiribella, G. M. D'Ariano, P. Perinotti, D. Schlingemann, and R. F. Werner, e-print arXiv: 0905.3801
    • G. Chiribella, G. M. D'Ariano, P. Perinotti, D. Schlingemann, and R. F. Werner, e-print arXiv: 0905.3801.
  • 69
    • 0001410138 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.79.321
    • M. A. Nielsen and I. L. Chuang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.321 79, 321 (1997).
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 321
    • Nielsen, M.A.1    Chuang, I.L.2
  • 71
    • 77954179201 scopus 로고    scopus 로고
    • S. Lloyd, e-print arXiv: quant-ph/0501135
    • S. Lloyd, e-print arXiv: quant-ph/0501135.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.