메뉴 건너뛰기




Volumn 59, Issue 2, 2013, Pages 803-817

Entropic inequalities and marginal problems

Author keywords

Entropic inequalities; marginal problem; polymatroids; quantum contextuality

Indexed keywords

ANALYTIC SOLUTION; CONTEXTUALITY; CONTINUOUS VARIABLES; CYCLE GRAPHS; DIFFERENTIAL ENTROPY; ENTROPIC INEQUALITIES; FOURIER-MOTZKIN ELIMINATION; GRAPHICAL MODEL; HYPERGRAPH; JOINT DISTRIBUTIONS; MARGINAL DISTRIBUTION; MARGINAL PROBLEM; MARGINALS; NONTRIVIAL CONDITIONS; POLYMATROIDS; QUANTUM NONLOCALITY; SHANNON ENTROPY; SOFTWARE INTERFACES;

EID: 84872699409     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2012.2222863     Document Type: Article
Times cited : (105)

References (64)
  • 1
    • 0000486090 scopus 로고
    • On the einstein-odolsky-rosen paradox
    • J. S. Bell, "On the Einstein-odolsky-Rosen paradox," Physics, vol. 1, pp. 195-200, 1964.
    • (1964) Physics , vol.1 , pp. 195-200
    • Bell, J.S.1
  • 2
    • 0000263339 scopus 로고
    • Hidden variables, joint probability, and the Bell inequalities
    • Feb
    • A. Fine, "Hidden variables, joint probability, and the Bell inequalities," Phys. Rev. Lett., vol. 48, no. 5, pp. 291-295, Feb. 1982.
    • (1982) Phys. Rev. Lett , vol.48 , Issue.5 , pp. 291-295
    • Fine, A.1
  • 3
    • 30344460132 scopus 로고
    • Experimental tests of realistic local theories via Bell's theorem
    • Aug
    • A. Aspect, P. Grangier, and G. Roger, "Experimental tests of realistic local theories via Bell's theorem," Phys. Rev. Lett., vol. 47, pp. 460-463, Aug. 1981.
    • (1981) Phys. Rev. Lett , vol.47 , pp. 460-463
    • Aspect, A.1    Grangier, P.2    Roger, G.3
  • 4
    • 83655197951 scopus 로고    scopus 로고
    • The sheaf-theoretic structure of non-locality and contextuality
    • S. Abramsky and A. Brandenburger, "The sheaf-theoretic structure of non-locality and contextuality," New J. Phys., vol. 13, no. 11, p. 113036, 2011.
    • (2011) New J. Phys , vol.13 , Issue.11 , pp. 113036
    • Abramsky, S.1    Brandenburger, A.2
  • 7
    • 80051895678 scopus 로고    scopus 로고
    • Specker's parable of the overprotective seer: A road to contextuality, nonlocality and complementarity
    • Y.-C. Liang, R. W. Spekkens, and H. M.Wiseman, "Specker's parable of the overprotective seer: A road to contextuality, nonlocality and complementarity," Phys. Rep., vol. 506, no. 1-2, pp. 1-39, 2011.
    • (2011) Phys. Rep , vol.506 , Issue.1-2 , pp. 1-39
    • Liang, Y.-C.1    Spekkens, R.W.2    Wiseman, H.M.3
  • 9
    • 3543080768 scopus 로고    scopus 로고
    • Ph.D. dissertation, Czech Tech. Univ., Faculty Electr. Eng. Prague, Czech Republic
    • J. Vomlel, Methods of probabilistic knowledge integration Ph.D. dissertation, Czech Tech. Univ., Faculty Electr. Eng. Prague, Czech Republic, 1999.
    • (1999) Methods of Probabilistic Knowledge Integration
    • Vomlel, J.1
  • 11
    • 0033349024 scopus 로고    scopus 로고
    • Disclosure detection in multivariate categorical databases: auditing confidentiality protection through two new matrix operators
    • S. D. Chowdhury, G. T. Duncan, R. Krishnan, S. F. Roehrig, and S. Mukherjee, "Disclosure detection in multivariate categorical databases: Auditing confidentiality protection through two new matrix operators," J. Manage. Sci., vol. 45, no. 12, pp. 1710-1723, 1999. (Pubitemid 30561199)
    • (1999) Management Science , vol.45 , Issue.12 , pp. 1710-1723
    • Chowdhury, S.D.1    Duncan, G.T.2    Krishnan, R.3    Roehrig, S.F.4    Mukherjee, S.5
  • 12
    • 70349305273 scopus 로고    scopus 로고
    • Differential privacy: A survey of results
    • Berlin, Germany
    • C. Dwork, "Differential privacy: A survey of results," in Proc. 5th Int. Conf. Theory Appl.Models Comput., Berlin, Germany, 2008, pp. 1-19.
    • (2008) Proc. 5th Int. Conf. Theory Appl.Models Comput , pp. 1-19
    • Dwork, C.1
  • 13
    • 84872722002 scopus 로고
    • Coalition games
    • N. N. Vorob'ev, "Coalition games," Theory Probab. Appl., vol. 12, pp. 251-266, 1967.
    • (1967) Theory Probab. Appl , vol.12 , pp. 251-266
    • Vorob'Ev, N.N.1
  • 14
    • 0012044294 scopus 로고
    • Sur la compatibilité des fonctions de répartition
    • J. Bass, "Sur la compatibilité des fonctions de répartition," C. R. Acad. Sci. Paris, vol. 240, pp. 839-841, 1955.
    • (1955) C. R. Acad. Sci. Paris , vol.240 , pp. 839-841
    • Bass, J.1
  • 15
    • 0011873303 scopus 로고
    • Sulla compatibilità delle funzioni di ripartizione doppia
    • G. Dall'Aglio, "Sulla compatibilità delle funzioni di ripartizione doppia," Rend. Mat. e Appl. (5), vol. 18, pp. 385-413, 1959.
    • (1959) Rend. Mat. e Appl. (5) , vol.18 , pp. 385-413
    • Dall'Aglio, G.1
  • 16
    • 33748644302 scopus 로고
    • Verteilungsfunktionen mit gegebenen Marginalverteilungen
    • H. G. Kellerer, "Verteilungsfunktionen mit gegebenen Marginalverteilungen," Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, vol. 3, pp. 247-270, 1964.
    • (1964) Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , vol.3 , pp. 247-270
    • Kellerer, H.G.1
  • 17
    • 0000607947 scopus 로고
    • Consistent families ofmeasures and their extensions
    • N. N.Vorob'ev, "Consistent families ofmeasures and their extensions," Theory Probab. Appl., vol. 7, no. 2, pp. 147-163, 1962.
    • (1962) Theory Probab. Appl , vol.7 , Issue.2 , pp. 147-163
    • Vorob'ev, N.N.1
  • 18
    • 78549291426 scopus 로고
    • The general marginal problem
    • D. Butkovic, S. Kurepa, and H. Kraljevic, Eds. Berlin, Germany: Springer-Verlag
    • J. Hoffmann-Jørgensen, "The general marginal problem," in Functional Analysis II, ser. Lecture Notes in Mathematics, D. Butkovic, S. Kurepa, and H. Kraljevic, Eds. Berlin, Germany: Springer-Verlag, 1987, vol. 1242, pp. 77-367.
    • (1987) Functional Analysis II, Ser. Lecture Notes in Mathematics , vol.1242 , pp. 77-367
    • Hoffmann-Jørgensen, J.1
  • 20
    • 36749094027 scopus 로고    scopus 로고
    • Functionally compatible local characteristics for the local specification of priors in graphical models
    • C. Asci and M. Piccioni, "Functionally compatible local characteristics for the local specification of priors in graphical models," Scand. J. Statist., vol. 34, no. 4, pp. 829-840, 2007.
    • (2007) Scand. J. Statist , vol.34 , Issue.4 , pp. 829-840
    • Asci, C.1    Piccioni, M.2
  • 21
    • 38249028672 scopus 로고
    • Existence of extensions and product extensions for discrete probability distributions
    • F. M. Malvestuto, "Existence of extensions and product extensions for discrete probability distributions," Discr. Math., vol. 69, no. 1, pp. 61-77, 1988.
    • (1988) Discr. Math , vol.69 , Issue.1 , pp. 61-77
    • Malvestuto, F.M.1
  • 22
    • 21844499872 scopus 로고
    • Marginal problem in different calculi of AI
    • M. Studený, "Marginal problem in different calculi of AI," in Proc. Adv. Intell. Comput., 1995, pp. 348-359.
    • (1995) Proc. Adv. Intell. Comput , pp. 348-359
    • Studený, M.1
  • 23
    • 33646436427 scopus 로고    scopus 로고
    • Quantum marginal problem and -representability
    • A. A. Klyachko, "Quantum marginal problem and -representability, " J. Phys.: Conf. Ser., vol. 36, pp. 72-86, 2006.
    • (2006) J. Phys.: Conf. ser , vol.36 , pp. 72-86
    • Klyachko, A.A.1
  • 24
    • 54749110342 scopus 로고    scopus 로고
    • Dualities between entropy functions and network codes
    • Oct
    • T. Chan and A. Grant, "Dualities between entropy functions and network codes," IEEE Trans. Inf. Theory, vol. 54, no. 10, pp. 4470-4487, Oct. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.10 , pp. 4470-4487
    • Chan, T.1    Grant, A.2
  • 27
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • May
    • E. T. Jaynes, "Information theory and statistical mechanics," Phys. Rev., vol. 106, pp. 620-630, May 1957.
    • (1957) Phys. Rev , vol.106 , pp. 620-630
    • Jaynes, E.T.1
  • 28
    • 79751469224 scopus 로고    scopus 로고
    • Digested information as an information theoretic motivation for social interaction
    • C. Salge and D. Polani, "Digested information as an information theoretic motivation for social interaction," J. Artif. Soc. Soc. Simulat., vol. 14, no. 1, pp. 5-27, 2011.
    • (2011) J. Artif. Soc. Soc. Simulat. , vol.14 , Issue.1 , pp. 5-27
    • Salge, C.1    Polani, D.2
  • 29
    • 77955775031 scopus 로고    scopus 로고
    • Sumset and inverse sumset theorems for shannon entropy
    • T. Tao, "Sumset and inverse sumset theorems for Shannon entropy," Combin. Probab. Comput., vol. 19, no. 4, pp. 603-639, 2010.
    • (2010) Combin. Probab. Comput , vol.19 , Issue.4 , pp. 603-639
    • Tao, T.1
  • 30
    • 77957602848 scopus 로고    scopus 로고
    • Information inequalities for joint distributions, with interpretations and applications
    • Jun
    • M. Madiman and P. Tetali, "Information inequalities for joint distributions, with interpretations and applications," IEEE Trans. Inf. Theory, vol. 56, no. 6, pp. 2699-2713, Jun. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.6 , pp. 2699-2713
    • Madiman, M.1    Tetali, P.2
  • 31
    • 0031268521 scopus 로고    scopus 로고
    • A framework for linear information inequalities
    • PII S0018944897068168
    • R.W. Yeung, "A framework for linear information inequalities," IEEE Trans. Inf. Theory, vol. 43, no. 6, pp. 1924-1934, Nov. 1997. (Pubitemid 127826482)
    • (1997) IEEE Transactions on Information Theory , vol.43 , Issue.6 , pp. 1924-1934
    • Yeung, R.W.1
  • 32
    • 0032124111 scopus 로고    scopus 로고
    • On characterization of entropy function via information inequalities
    • PII S001894489803630X
    • Z. Zhang and R. Yeung, "On characterization of entropy function via information inequalities," IEEE Trans. Inf. Theory, vol. 44, no. 4, pp. 1440-1452, Jul. 1998. (Pubitemid 128736707)
    • (1998) IEEE Transactions on Information Theory , vol.44 , Issue.4 , pp. 1440-1452
    • Zhang, Z.1    Yeung, R.W.2
  • 33
    • 0036648210 scopus 로고    scopus 로고
    • On a relation between information inequalities and group theory
    • Jul
    • T. Chan and R. Yeung, "On a relation between information inequalities and group theory," IEEE Trans. Inf. Theory, vol. 48, no. 7, pp. 1992-1995, Jul. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.7 , pp. 1992-1995
    • Chan, T.1    Yeung, R.2
  • 35
    • 35949013249 scopus 로고
    • Information-theoretic bell inequalities
    • S. L. Braunstein and C.M. Caves, "Information-theoretic Bell inequalities," Phys. Rev. Lett., vol. 61, pp. 662-665, 1988.
    • (1988) Phys. Rev. Lett , vol.61 , pp. 662-665
    • Braunstein, S.L.1    Caves, C.M.2
  • 36
    • 84858425958 scopus 로고    scopus 로고
    • Entropic approach to local realism and noncontextuality
    • R. Chaves and T. Fritz, "Entropic approach to local realism and noncontextuality," Phys. Rev. A, vol. 85, pp. 032113-1-032113-11, 2012.
    • (2012) Phys. Rev. A , vol.85 , pp. 032113-032111
    • Chaves, R.1    Fritz, T.2
  • 37
    • 84872716411 scopus 로고    scopus 로고
    • Ed. Champaign IL
    • MATHEMATICA6.0 ed. Champaign, IL, 2007.
    • (2007) MATHEMATICA6.0
  • 41
    • 51249163663 scopus 로고
    • Some advances in the study of the compatibility of three bivariate copulas
    • J. Quesada-Molina and J. Rodríguez-Lallena, "Some advances in the study of the compatibility of three bivariate copulas," Statist. Methods Appl., vol. 3, pp. 397-417, 1994.
    • (1994) Statist. Methods Appl , vol.3 , pp. 397-417
    • Quesada-Molina, J.1    Rodríguez-Lallena, J.2
  • 44
    • 0003084082 scopus 로고
    • The problem of hidden variables in quantum mechanics
    • S. Kochen and E. P. Specker, "The problem of hidden variables in quantum mechanics," J. Math. Mech., vol. 17, pp. 59-87, 1967.
    • (1967) J. Math. Mech , vol.17 , pp. 59-87
    • Kochen, S.1    Specker, E.P.2
  • 45
    • 77951134661 scopus 로고    scopus 로고
    • Nonlocality and communication complexity
    • Mar
    • H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, "Nonlocality and communication complexity," Rev. Mod. Phys., vol. 82, pp. 665-698, Mar. 2010.
    • (2010) Rev. Mod. Phys , vol.82 , pp. 665-698
    • Buhrman, H.1    Cleve, R.2    Massar, S.3    De Wolf, R.4
  • 47
    • 66549107253 scopus 로고    scopus 로고
    • Device-independent quantum key distribution secure against collective attacks
    • S. Pironio, A. Acin, N. Brunner, N. Gisin, S. Massar, and V. Scarani, "Device-independent quantum key distribution secure against collective attacks," New J. Phys., vol. 11, no. 4, p. 045021, 2009.
    • (2009) New J. Phys , vol.11 , Issue.4 , pp. 045021
    • Pironio, S.1    Acin, A.2    Brunner, N.3    Gisin, N.4    Massar, S.5    Scarani, V.6
  • 48
    • 84872740644 scopus 로고
    • A value for -erson games
    • H. Kuhn and A. Tucker, Eds. Princeton, NJ: Princeton Univ. Press
    • L. S. Shapley, "A value for -erson games," in Contributions to the Theory of Games, H. Kuhn and A. Tucker, Eds. Princeton, NJ: Princeton Univ. Press, 1953.
    • (1953) Contributions to the Theory of Games
    • Shapley, L.S.1
  • 50
    • 84971795889 scopus 로고
    • Recognizing polymatroids associated with hypergraphs
    • D. Vertigan and G. Whittle, "Recognizing polymatroids associated with hypergraphs," Combin. Probab. Comput., vol. 2, no. 4, pp. 519-530, 1993.
    • (1993) Combin. Probab. Comput , vol.2 , Issue.4 , pp. 519-530
    • Vertigan, D.1    Whittle, G.2
  • 51
    • 0003104050 scopus 로고
    • Optimal flows in networks with multiple sources and sinks
    • N. Megiddo, "Optimal flows in networks with multiple sources and sinks," Math. Programm., vol. 7, pp. 97-107, 1974.
    • (1974) Math. Programm , vol.7 , pp. 97-107
    • Megiddo, N.1
  • 53
    • 0347367241 scopus 로고    scopus 로고
    • Extremality of submodular functions
    • K. Kashiwabara, "Extremality of submodular functions," Theoret. Comput. Sci., vol. 235, no. 2, pp. 239-256, 2000.
    • (2000) Theoret. Comput. Sci , vol.235 , Issue.2 , pp. 239-256
    • Kashiwabara, K.1
  • 54
    • 34250468778 scopus 로고    scopus 로고
    • Cores of convex games
    • L. S. Shapley, "Cores of convex games," Int. J. Game Theory, vol. 1, pp. 11-26.
    • Int. J. Game Theory , vol.1 , pp. 11-26
    • Shapley, L.S.1
  • 56
    • 0001327106 scopus 로고
    • Fourier'smethod of linear programming and its dual
    • H. P.Williams, "Fourier'smethod of linear programming and its dual," Amer. Math. Monthly, vol. 93, no. 9, pp. 681-695, 1986.
    • (1986) Amer. Math. Monthly , vol.93 , Issue.9 , pp. 681-695
    • Williams, H.P.1
  • 57
    • 84872732062 scopus 로고    scopus 로고
    • [Online]
    • R. Chaves and T. Fritz, 2011[Online]. Available: http://users.icfo.es/ Tobias.Fritz/2011/input-for-porta.nb
    • (2011)
    • Chaves, R.1    Fritz, T.2
  • 58
    • 0035601976 scopus 로고    scopus 로고
    • Decomposition and parallelization techniques for enumerating the facets of combinatorial polytopes
    • DOI 10.1142/S0218195901000560
    • T. Christof and G. Reinelt, "Decomposition and parallelization techniques for enumerating the facets of combinatorial polytopes," Int. J. Comput. Geom. Appl., vol. 11, no. 4, pp. 423-437, 2001. (Pubitemid 33677113)
    • (2001) International Journal of Computational Geometry and Applications , vol.11 , Issue.4 , pp. 423-437
    • Christof, T.1    Reinelt, G.2
  • 61
    • 48249090439 scopus 로고    scopus 로고
    • Simple test for hidden variables in spin-1 systems
    • A. A. Klyachko, M. A. Can, S. Binicioǧlu, and A. S. Shumovsky, "Simple test for hidden variables in spin-1 systems," Phys. Rev. Lett., vol. 101, pp. 020403-1-020403-4, 2008.
    • (2008) Phys. Rev. Lett , vol.101 , pp. 020403-020401
    • Klyachko, A.A.1    Can, M.A.2    Binicioǧlu, S.3    Shumovsky, A.S.4
  • 63
    • 0346707320 scopus 로고    scopus 로고
    • Balanced information inequalities
    • Dec
    • T. Chan, "Balanced information inequalities," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3261-3267, Dec. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 3261-3267
    • Chan, T.1
  • 64
    • 0031276041 scopus 로고    scopus 로고
    • A non-shannon-type conditional inequality of information quantities
    • PII S0018944897072957
    • Z. Zhang and R. Yeung, "A non-Shannon-type conditional inequality of information quantities," IEEE Trans. Inf. Theory, vol. 43, no. 6, pp. 1982-1986, Nov. 1997 (Pubitemid 127826487)
    • (1997) IEEE Transactions on Information Theory , vol.43 , Issue.6 , pp. 1982-1986
    • Zhang, Z.1    Yeung, R.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.