Edit Profile (opens in new tab) Petz, Dénes (b. 1953 d. 2018) Co-Author Distance Author ID: petz.denes Published as: Petz, Dénes; Petz, D.; Petz, Denes; Petz, Dènes; Petz, Dénez more...less Homepage: http://math.bme.hu/~petz/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef Documents Indexed: 161 Publications since 1977, including 6 Books and 3 Additional arXiv Preprints 1 Further Contribution Reviewing Activity: 88 Reviews Biographic References: 1 Publication Co-Authors: 53 Co-Authors with 97 Joint Publications 1,053 Co-Co-Authors all top 5 Co-Authors 63 single-authored 36 Hiai, Fumio 6 Cecchini, Carlo 6 Ohya, Masanori 5 Mosonyi, Milán 5 Szántó, András 4 Besenyei, Ádám 4 Hangos, Katalin Mária 4 Ohno, Hiromichi 4 Ruppert, László 3 Jenčová, Anna 3 Ruskai, Mary Beth 3 Ueda, Yoshimichi 2 Baier, Thomas 2 Bény, Cédric 2 Fannes, Mark 2 Gibilisco, Paolo 2 Magyar, Attila 2 Pitrik, József 2 Réffy, Júlia 2 Sudár, Csaba 2 Toth, Gabor 2 Virosztek, Dániel 2 Watanabe, Noboru 1 Akiho, Nobuyuki 1 Andai, Attila 1 Ando, Tsuyoshi 1 Audenaert, Koenraad M. R. 1 Bródy, F. 1 Császár, Ákos E. 1 Csiszár, Imre 1 Fritz, József 1 Geszti, Tamás 1 Ghinea, Cătălin 1 Hasegawa, Hiroshi H. 1 Hayden, Patrick M. 1 Jozsa, Richard 1 Kahn, Jonas 1 Kim, Sejong 1 Kosaki, Hideki 1 Léka, Zoltán 1 Michor, Peter Wolfram 1 Mizuo, Masaru 1 Muraki, Naohumi 1 Nielsen, Michael A. 1 Pálfia, Miklós 1 Pérez-García, David 1 Raggio, Guido A. 1 Rédei, M. R. 1 Szabó, V. E. Sándor 1 Szöllősi, Ferenc 1 Temesi, Róbert 1 Tóth, Géza 1 Vámos, Tibor 1 Verbeure, André F. 1 Weiner, Mihály 1 Winter, Andreas 1 Wolf, Michael Marc 1 Zemánek, Jaroslav all top 5 Serials 11 Acta Scientiarum Mathematicarum 10 Linear Algebra and its Applications 9 Journal of Mathematical Physics 8 Acta Mathematica Hungarica 7 Communications in Mathematical Physics 7 Reviews in Mathematical Physics 6 Studia Scientiarum Mathematicarum Hungarica 5 Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 Letters in Mathematical Physics 4 Reports on Mathematical Physics 4 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica 3 Journal of Functional Analysis 3 Probability Theory and Related Fields 2 Acta Mathematica Academiae Scientiarum Hungaricae 2 IEEE Transactions on Information Theory 2 Matematikai Lapok 2 Proceedings of the American Mathematical Society 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Probability and Mathematical Statistics 2 Journal of Physics A: Mathematical and General 2 Journal of Physics A: Mathematical and Theoretical 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Linear and Multilinear Algebra 1 Periodica Mathematica Hungarica 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Commentationes Mathematicae Universitatis Carolinae 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Rivista di Matemàtica Pura ed Applicata 1 SIAM Journal on Matrix Analysis and Applications 1 International Journal of Mathematics 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Open Systems & Information Dynamics 1 Mathematical Inequalities & Applications 1 Entropy 1 Quantum Information Processing 1 Leuven Notes in Mathematical and Theoretical Physics 1 Mathematical Surveys and Monographs 1 World Scientific Series in 20th Century Mathematics 1 Texts and Readings in Mathematics 1 Annales Mathematicae et Informaticae 1 Operators and Matrices 1 Quantum Information & Computation 1 Journal of Applied Mathematics & Informatics 1 Universitext 1 Theoretical and Mathematical Physics (Cham) 1 Texts and Monographs in Physics all top 5 Fields 72 Functional analysis (46-XX) 58 Quantum theory (81-XX) 36 Information and communication theory, circuits (94-XX) 32 Linear and multilinear algebra; matrix theory (15-XX) 25 Probability theory and stochastic processes (60-XX) 22 Operator theory (47-XX) 17 Statistical mechanics, structure of matter (82-XX) 14 Statistics (62-XX) 9 General topology (54-XX) 7 Real functions (26-XX) 6 Differential geometry (53-XX) 3 Sequences, series, summability (40-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 131 Publications have been cited 3,065 times in 1,817 Documents Cited by ▼ Year ▼ Quantum entropy and its use. Zbl 0891.94008 Ohya, Masanori; Petz, Dénes 329 1993 The semicircle law, free random variables and entropy. Zbl 0955.46037 Hiai, Fumio; Petz, Dénes 205 2000 Quantum information theory and quantum statistics. Zbl 1145.81002 Petz, Dénes 183 2008 Quasi-entropies for finite quantum systems. Zbl 0629.46061 Petz, Dénes 166 1986 Monotone metrics on matrix spaces. Zbl 0856.15023 Petz, Dénes 160 1996 Structure of states which satisfy strong subadditivity of quantum entropy with equality. Zbl 1126.82004 Hayden, Patrick; Jozsa, Richard; Petz, Dénes; Winter, Andreas 123 2004 The proper formula for relative entropy and its asymptotics in quantum probability. Zbl 0756.46043 Hiai, Fumio; Petz, Dénes 117 1991 Sufficient subalgebras and the relative entropy of states of a von Neumann algebra. Zbl 0597.46067 Petz, Dénes 100 1986 Sufficiency of channels over von Neumann algebras. Zbl 0644.46041 Petz, Dénes 91 1988 Quantum \(f\)-divergences and error correction. Zbl 1230.81007 Hiai, Fumio; Mosonyi, Milán; Petz, Dénes; Bény, Cédric 81 2011 Introduction to matrix analysis and applications. Zbl 1303.15001 Hiai, Fumio; Petz, Dénes 72 2014 Geometries of quantum states. Zbl 0868.60098 Petz, Dénes; Sudár, Csaba 69 1996 The Golden-Thompson trace inequality is complemented. Zbl 0784.15011 Hiai, Fumio; Petz, Dénes 63 1993 Monotonicity of quantum relative entropy revisited. Zbl 1134.82303 Petz, Dénez 58 2003 An invitation to the algebra of canonical commutation relations. Zbl 0704.46045 Petz, Dénes 55 1990 Quasi-entropies for states of a von Neumann algebra. Zbl 0606.46039 Petz, Dénes 55 1985 Sufficiency in quantum statistical inference. Zbl 1156.81325 Jenčová, Anna; Petz, Dénes 54 2006 Geometry of canonical correlation on the state space of a quantum system. Zbl 0804.53101 Petz, Dénes 40 1994 Contractivity of positive and trace-preserving maps under \(L_{p}\) norms. Zbl 1112.15007 Pérez-García, David; Wolf, Michael M.; Petz, Denes; Ruskai, Mary Beth 38 2006 On the Riemannian metric of \(\alpha\)-entropies of density matrices. Zbl 0855.58070 Petz, Dénes; Hasegawa, Hiroshi 38 1996 Logarithmic energy as an entropy functional. Zbl 0893.15011 Petz, Dénes; Hiai, Fumio 36 1998 The Bogoliubov inner product in quantum statistics. Zbl 0773.53056 Petz, Dénes; Toth, Gabor 30 1993 Introduction to quantum Fisher information. Zbl 1257.81015 Petz, D.; Ghinea, C. 29 2011 A survey of certain trace inequalities. Zbl 0802.15012 Petz, Dénes 27 1994 Asymptotic of Varadhan-type and the Gibbs variational principle. Zbl 0682.46054 Petz, D.; Raggio, G. A.; Verbeure, A. 26 1989 Spectral scale of selfadjoint operators and trace inequalities. Zbl 0655.47032 Petz, Dénes 26 1985 A variational expression for the relative entropy. Zbl 0663.46069 Petz, Dénes 25 1988 Covariance and Fisher information in quantum mechanics. Zbl 1168.81317 Petz, Dénes 25 2002 Riemannian metrics on positive definite matrices related to means. Zbl 1163.53011 Hiai, Fumio; Petz, Dénes 23 2009 From quasi-entropy to various quantum information quantities. Zbl 1256.81024 Hiai, Fumio; Petz, Dénes 20 2012 Characterizations of the trace. Zbl 0661.15017 Petz, Dénes; Zemánek, Jaroslav 20 1988 Complementarity in quantum systems. Zbl 1143.81302 Petz, Dénes 19 2007 A dual in von Neumann algebras with weights. Zbl 0571.46042 Petz, Dénes 19 1984 Means of positive numbers and matrices. Zbl 1108.47020 Petz, Dénes; Temesi, Róbert 19 2005 Sufficiency in quantum statistical inference: a survey with examples. Zbl 1108.46045 Jenčová, Anna; Petz, Dénes 19 2006 Riemannian metrics on positive definite matrices related to means. II. Zbl 1309.53017 Hiai, Fumio; Petz, Dénes 18 2012 On capacities of quantum channels. Zbl 0880.60102 Ohya, Masanori; Petz, Dénes; Watanabe, Noboru 18 1997 Structure of sufficient quantum coarse-grainings. Zbl 1055.81012 Mosonyi, Milán; Petz, Dénes 18 2004 Contraction of generalized relative entropy under stochastic mappings on matrices. Zbl 0917.94006 Petz, Dénes; Ruskai, Mary Beth 17 1998 A simple proof of the strong subadditivity inequality. Zbl 1175.82009 Nielsen, M. A.; Petz, D. 17 2005 Entropy densities for algebraic states. Zbl 0816.46060 Hiai, Fumio; Petz, Dénes 17 1994 A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices. Zbl 0954.60030 Hiai, Fumio; Petz, Dénes 16 2000 From \(f\)-divergence to quantum quasi-entropies and their use. Zbl 1229.81054 Petz, Dénes 16 2010 Introduction to matrix analysis and applications. Zbl 1321.15004 Hiai, Fumio; Petz, Dénes 16 2014 Asymptotic freeness almost everywhere for random matrices. Zbl 0973.15016 Hiai, Fumio; Petz, Dénes 15 2000 On asymptotics of large Haar distributed unitary matrices. Zbl 1092.15021 Petz, Dénes; Réffy, Júlia 15 2004 Free transportation cost inequalities via random matrix approximation. Zbl 1060.46046 Hiai, Fumio; Petz, Dénes; Ueda, Yoshimichi 15 2004 Families of completely positive maps associated with monotone metrics. Zbl 1300.15009 Hiai, Fumio; Kosaki, Hideki; Petz, Dénes; Ruskai, Mary Beth 13 2013 Eigenvalue density of the Wishart matrix and large deviations. Zbl 0934.60006 Hiai, Fumio; Petz, Dénes 12 1998 Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices. Zbl 1076.60022 Petz, Dénes; Réffy, Júlia 11 2005 Quantum covariance, quantum Fisher information, and the uncertainty relations. Zbl 1367.81025 Gibilisco, Paolo; Hiai, Fumio; Petz, Dénes 11 2009 Complementarity and the algebraic structure of four-level quantum systems. Zbl 1191.47086 Petz, Dénes; Szántó, András; Weiner, Mihály 11 2009 Properties of the relative entropy of states of von Neumann algebras. Zbl 0656.46049 Petz, D. 11 1986 Large deviations for functions of two random projection matrices. Zbl 1121.15024 Hiai, Fumio; Petz, Dénes 10 2006 Entropies of general quantum states. Zbl 0961.81509 Muraki, Naohumi; Ohya, Masanori; Petz, Dénes 10 1992 Point estimation of states of finite quantum systems. Zbl 1119.81039 Petz, D.; Hangos, K. M.; Magyar, Attila 10 2007 Some inequalities for quantum Tsallis entropy related to the strong subadditivity. Zbl 1345.46052 Petz, Dénes; Virosztek, Dániel 10 2015 Bregman divergence as relative operator entropy. Zbl 1135.94318 Petz, D. 9 2007 Quasi-orthogonal subalgebras of \(4 \times 4\) matrices. Zbl 1120.15013 Ohno, Hiromichi; Petz, Dénes; Szántó, András 9 2007 Ergodic theorems in von Neumann algebras. Zbl 0535.46043 Petz, Dénes 9 1983 Completely positive mappings and mean matrices. Zbl 1223.26048 Besenyei, Ádám; Petz, Dénes 9 2011 On the equality in Jensen’s inequality for operator convex functions. Zbl 0638.46040 Petz, Dénes 9 1986 State extensions and a Radon-Nikodým theorem for conditional expectations on von Neumann algebras. Zbl 0695.46024 Cecchini, Carlo; Petz, Dénes 9 1989 Complementary reductions for two qubits. Zbl 1112.81020 Petz, Dénes; Kahn, Jonas 8 2007 Numerical computation of quantum capacity. Zbl 0963.81011 Ohya, Masanori; Petz, Dénes; Watanabe, Noboru 8 1998 Characterization of the relative entropy of states of matrix algebras. Zbl 0765.46045 Petz, D. 8 1992 Entropy densities for Gibbs states of quantum spin systems. Zbl 0791.60100 Hiai, Fumio; Petz, Dénes 8 1993 Means of positive matrices: geometry and a conjecture. Zbl 1115.47018 Petz, Dénes 7 2005 Generalizations of Pauli channels. Zbl 1265.15042 Ohno, H.; Petz, D. 7 2009 The Neumann compendium. Zbl 0829.01029 7 1995 Free energy density for mean field perturbation of states of a one-dimensional spin chain. Zbl 1153.82002 Hiai, Fumio; Mosonyi, Milán; Ohno, Hiromichi; Petz, Dénes 7 2008 Quasi-uniform ergodic theorems in von Neumann algebras. Zbl 0535.46042 Petz, Dénes 7 1984 Markov triplets on CCR-algebras. Zbl 1240.46095 Jenčová, Anna; Petz, Dénes; Pitrik, József 7 2010 A de Finetti-type theorem with m-dependent states. Zbl 0669.46034 Petz, Dénes 7 1990 Conditional expectation in quantum probability. Zbl 0649.46056 Petz, Dènes 7 1988 On the eigenvalue distribution of some symmetric random matrices. Zbl 0889.15006 Oravecz, F.; Petz, D. 6 1997 State tomography for two qubits using reduced densities. Zbl 1100.81013 Petz, D.; Hangos, K. M.; Szántó, A.; Szöllősi, F. 6 2006 Convexity of quasi-entropy type functions: Lieb’s and Ando’s convexity theorems revisited. Zbl 1282.81050 Hiai, Fumio; Petz, Dénes 6 2013 On certain properties of the relative entropy of states of operator algebras. Zbl 0707.46043 Petz, Denes 6 1991 From quasi-entropy to skew information. Zbl 1177.94112 Petz, D.; Szabó, V. E. S. 6 2009 A characterization of the class of compact Hausdorff spaces. Zbl 0448.54023 Petz, D. 5 1977 Efficient quantum tomography needs complementary and symmetric measurements. Zbl 1247.81081 Petz, Dénes; Ruppert, László 5 2012 Partial subadditivity of entropies. Zbl 1281.94009 Besenyei, Ádám; Petz, Dénes 5 2013 Weighted multivariable operator means of positive definite operators. Zbl 1314.47026 Pálfia, Miklós; Petz, Dénes 5 2014 Notes on quantum entropy. Zbl 0865.46043 Ohya, M.; Petz, D. 5 1996 Stationary quantum source coding. Zbl 1016.81017 Petz, Dénes; Mosonyi, Milán 5 2001 Jensen’s inequality for positive contractions on operator algebras. Zbl 0622.46044 Petz, Dénes 5 1987 Generalized connectednesses and disconnectednesses in topology. Zbl 0475.54009 Petz, D. 4 1981 On the function \(\text{Tr} e^{H+itK}\). Zbl 1001.15003 Fannes, Mark; Petz, Dénes 4 2002 Classes of conditional expectations over von Neumann algebras. Zbl 0718.46038 Cecchini, Carlo; Petz, Dénes 4 1990 Perturbation of Wigner matrices and a conjecture. Zbl 1025.15035 Fannes, Mark; Petz, Dénes 4 2003 Free relative entropy for measures and a corresponding perturbation theory. Zbl 1033.46051 Hiai, Fumio; Mizuo, Masaru; Petz, Dénes 4 2002 On the curvature of a certain Riemannian space of matrices. Zbl 1031.53109 Michor, Peter W.; Petz, Dénes; Andai, Attila 4 2000 Quantum mechanics in AF \(C^*\)-systems. Zbl 0948.81023 Hiai, Fumio; Petz, Dénes 4 1996 First steps towards a Donsker and Varadhan theory in operator algebras. Zbl 0713.60038 Petz, Dénes 4 1990 Comparison of some methods of quantum state estimation. Zbl 1139.81013 Baier, Th.; Petz, D.; Hangos, K. M.; Magyar, Attila 3 2007 Strongly subadditive functions. Zbl 1262.47024 Audenaert, K.; Hiai, F.; Petz, D. 3 2010 Optimal quantum-state tomography with known parameters. Zbl 1241.81039 Petz, Dénes; Ruppert, László 3 2012 From quasi-entropy. Zbl 1289.94036 Petz, Dénes 3 2012 Properties of free entropy related to polar decomposition. Zbl 0934.46063 Hiai, Fumio; Petz, Dénes 3 1999 Erratum to: “Quantum \(f\)-divergences and error correction”. Zbl 1447.81025 Hiai, Fumio; Mosonyi, Milán; Petz, Dénes; Bény, Cédric 1 2017 Some inequalities for quantum Tsallis entropy related to the strong subadditivity. Zbl 1345.46052 Petz, Dénes; Virosztek, Dániel 10 2015 Introduction to matrix analysis and applications. Zbl 1303.15001 Hiai, Fumio; Petz, Dénes 72 2014 Introduction to matrix analysis and applications. Zbl 1321.15004 Hiai, Fumio; Petz, Dénes 16 2014 Weighted multivariable operator means of positive definite operators. Zbl 1314.47026 Pálfia, Miklós; Petz, Dénes 5 2014 Conditional SIC-POVMs. Zbl 1364.81067 Petz, Dénes; Ruppert, László; Szántó, András 3 2014 Families of completely positive maps associated with monotone metrics. Zbl 1300.15009 Hiai, Fumio; Kosaki, Hideki; Petz, Dénes; Ruskai, Mary Beth 13 2013 Convexity of quasi-entropy type functions: Lieb’s and Ando’s convexity theorems revisited. Zbl 1282.81050 Hiai, Fumio; Petz, Dénes 6 2013 Partial subadditivity of entropies. Zbl 1281.94009 Besenyei, Ádám; Petz, Dénes 5 2013 Successive iterations and logarithmic means. Zbl 1266.15029 Besenyei, Ádám; Petz, Dénes 2 2013 Some decompositions of matrix variances. Zbl 1429.62313 Léka, Zoltán; Petz, Dénes 1 2013 From quasi-entropy to various quantum information quantities. Zbl 1256.81024 Hiai, Fumio; Petz, Dénes 20 2012 Riemannian metrics on positive definite matrices related to means. II. Zbl 1309.53017 Hiai, Fumio; Petz, Dénes 18 2012 Efficient quantum tomography needs complementary and symmetric measurements. Zbl 1247.81081 Petz, Dénes; Ruppert, László 5 2012 Optimal quantum-state tomography with known parameters. Zbl 1241.81039 Petz, Dénes; Ruppert, László 3 2012 From quasi-entropy. Zbl 1289.94036 Petz, Dénes 3 2012 Matrix variances with projections. Zbl 1289.81006 Petz, Dénes; Tóth, Géza 2 2012 Quantum \(f\)-divergences and error correction. Zbl 1230.81007 Hiai, Fumio; Mosonyi, Milán; Petz, Dénes; Bény, Cédric 81 2011 Introduction to quantum Fisher information. Zbl 1257.81015 Petz, D.; Ghinea, C. 29 2011 Completely positive mappings and mean matrices. Zbl 1223.26048 Besenyei, Ádám; Petz, Dénes 9 2011 From \(f\)-divergence to quantum quasi-entropies and their use. Zbl 1229.81054 Petz, Dénes 16 2010 Markov triplets on CCR-algebras. Zbl 1240.46095 Jenčová, Anna; Petz, Dénes; Pitrik, József 7 2010 Strongly subadditive functions. Zbl 1262.47024 Audenaert, K.; Hiai, F.; Petz, D. 3 2010 Complementarity and state estimation. Zbl 1202.81011 Baier, Thomas; Petz, Dénes 2 2010 Algebraic complementarity in quantum theory. Zbl 1247.81026 Petz, Dénes 2 2010 Hilbert space methods for quantum mechanics. Zbl 1208.81058 Petz, D. 1 2010 Riemannian metrics on positive definite matrices related to means. Zbl 1163.53011 Hiai, Fumio; Petz, Dénes 23 2009 Quantum covariance, quantum Fisher information, and the uncertainty relations. Zbl 1367.81025 Gibilisco, Paolo; Hiai, Fumio; Petz, Dénes 11 2009 Complementarity and the algebraic structure of four-level quantum systems. Zbl 1191.47086 Petz, Dénes; Szántó, András; Weiner, Mihály 11 2009 Generalizations of Pauli channels. Zbl 1265.15042 Ohno, H.; Petz, D. 7 2009 From quasi-entropy to skew information. Zbl 1177.94112 Petz, D.; Szabó, V. E. S. 6 2009 Gaussian Markov triplets approached by block matrices. Zbl 1212.60129 Ando, Tsuyoshi; Petz, Dénes 3 2009 Markov property of Gaussian states of canonical commutation relation algebras. Zbl 1304.81104 Petz, Dénes; Pitrik, József 3 2009 Quantum information theory and quantum statistics. Zbl 1145.81002 Petz, Dénes 183 2008 Free energy density for mean field perturbation of states of a one-dimensional spin chain. Zbl 1153.82002 Hiai, Fumio; Mosonyi, Milán; Ohno, Hiromichi; Petz, Dénes 7 2008 Quantum state tomography with finite sample size. Zbl 1329.81150 Petz, Dénes; Hangos, Katalin M.; Ruppert, László 2 2008 Complementarity in quantum systems. Zbl 1143.81302 Petz, Dénes 19 2007 Point estimation of states of finite quantum systems. Zbl 1119.81039 Petz, D.; Hangos, K. M.; Magyar, Attila 10 2007 Bregman divergence as relative operator entropy. Zbl 1135.94318 Petz, D. 9 2007 Quasi-orthogonal subalgebras of \(4 \times 4\) matrices. Zbl 1120.15013 Ohno, Hiromichi; Petz, Dénes; Szántó, András 9 2007 Complementary reductions for two qubits. Zbl 1112.81020 Petz, Dénes; Kahn, Jonas 8 2007 Comparison of some methods of quantum state estimation. Zbl 1139.81013 Baier, Th.; Petz, D.; Hangos, K. M.; Magyar, Attila 3 2007 Limit relation for quantum entropy and channel capacity per unit cost. Zbl 1152.81388 Csiszár, Imre; Hiai, Fumio; Petz, Dénes 1 2007 Sufficiency in quantum statistical inference. Zbl 1156.81325 Jenčová, Anna; Petz, Dénes 54 2006 Contractivity of positive and trace-preserving maps under \(L_{p}\) norms. Zbl 1112.15007 Pérez-García, David; Wolf, Michael M.; Petz, Denes; Ruskai, Mary Beth 38 2006 Sufficiency in quantum statistical inference: a survey with examples. Zbl 1108.46045 Jenčová, Anna; Petz, Dénes 19 2006 Large deviations for functions of two random projection matrices. Zbl 1121.15024 Hiai, Fumio; Petz, Dénes 10 2006 State tomography for two qubits using reduced densities. Zbl 1100.81013 Petz, D.; Hangos, K. M.; Szántó, A.; Szöllősi, F. 6 2006 A free logarithmic Sobolev inequality on the circle. Zbl 1107.46044 Hiai, Fumio; Petz, Dénes; Ueda, Yoshimichi 2 2006 Saturation of an entropy bound and quantum Markov states. Zbl 1151.81317 Petz, D. 1 2006 Means of positive numbers and matrices. Zbl 1108.47020 Petz, Dénes; Temesi, Róbert 19 2005 A simple proof of the strong subadditivity inequality. Zbl 1175.82009 Nielsen, M. A.; Petz, D. 17 2005 Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices. Zbl 1076.60022 Petz, Dénes; Réffy, Júlia 11 2005 Means of positive matrices: geometry and a conjecture. Zbl 1115.47018 Petz, Dénes 7 2005 Structure of states which satisfy strong subadditivity of quantum entropy with equality. Zbl 1126.82004 Hayden, Patrick; Jozsa, Richard; Petz, Dénes; Winter, Andreas 123 2004 Structure of sufficient quantum coarse-grainings. Zbl 1055.81012 Mosonyi, Milán; Petz, Dénes 18 2004 On asymptotics of large Haar distributed unitary matrices. Zbl 1092.15021 Petz, Dénes; Réffy, Júlia 15 2004 Free transportation cost inequalities via random matrix approximation. Zbl 1060.46046 Hiai, Fumio; Petz, Dénes; Ueda, Yoshimichi 15 2004 Monotonicity of quantum relative entropy revisited. Zbl 1134.82303 Petz, Dénez 58 2003 Perturbation of Wigner matrices and a conjecture. Zbl 1025.15035 Fannes, Mark; Petz, Dénes 4 2003 Covariance and Fisher information in quantum mechanics. Zbl 1168.81317 Petz, Dénes 25 2002 On the function \(\text{Tr} e^{H+itK}\). Zbl 1001.15003 Fannes, Mark; Petz, Dénes 4 2002 Free relative entropy for measures and a corresponding perturbation theory. Zbl 1033.46051 Hiai, Fumio; Mizuo, Masaru; Petz, Dénes 4 2002 Stationary quantum source coding. Zbl 1016.81017 Petz, Dénes; Mosonyi, Milán 5 2001 The semicircle law, free random variables and entropy. Zbl 0955.46037 Hiai, Fumio; Petz, Dénes 205 2000 A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices. Zbl 0954.60030 Hiai, Fumio; Petz, Dénes 16 2000 Asymptotic freeness almost everywhere for random matrices. Zbl 0973.15016 Hiai, Fumio; Petz, Dénes 15 2000 On the curvature of a certain Riemannian space of matrices. Zbl 1031.53109 Michor, Peter W.; Petz, Dénes; Andai, Attila 4 2000 Properties of free entropy related to polar decomposition. Zbl 0934.46063 Hiai, Fumio; Petz, Dénes 3 1999 Extending the Fisher metric to density matrices. Zbl 0939.62008 Petz, D.; Sudár, Cs. 2 1999 Logarithmic energy as an entropy functional. Zbl 0893.15011 Petz, Dénes; Hiai, Fumio 36 1998 Contraction of generalized relative entropy under stochastic mappings on matrices. Zbl 0917.94006 Petz, Dénes; Ruskai, Mary Beth 17 1998 Eigenvalue density of the Wishart matrix and large deviations. Zbl 0934.60006 Hiai, Fumio; Petz, Dénes 12 1998 Numerical computation of quantum capacity. Zbl 0963.81011 Ohya, Masanori; Petz, Dénes; Watanabe, Noboru 8 1998 Maximizing free entropy. Zbl 0913.94003 Hiai, F.; Petz, D. 2 1998 On capacities of quantum channels. Zbl 0880.60102 Ohya, Masanori; Petz, Dénes; Watanabe, Noboru 18 1997 On the eigenvalue distribution of some symmetric random matrices. Zbl 0889.15006 Oravecz, F.; Petz, D. 6 1997 Monotone metrics on matrix spaces. Zbl 0856.15023 Petz, Dénes 160 1996 Geometries of quantum states. Zbl 0868.60098 Petz, Dénes; Sudár, Csaba 69 1996 On the Riemannian metric of \(\alpha\)-entropies of density matrices. Zbl 0855.58070 Petz, Dénes; Hasegawa, Hiroshi 38 1996 Notes on quantum entropy. Zbl 0865.46043 Ohya, M.; Petz, D. 5 1996 Quantum mechanics in AF \(C^*\)-systems. Zbl 0948.81023 Hiai, Fumio; Petz, Dénes 4 1996 Curvature in the geometry of canonical correlation. Zbl 0862.53016 Hiai, F.; Petz, D.; Tóth, G. 3 1996 The Neumann compendium. Zbl 0829.01029 7 1995 McMillan type convergence for quantum Gibbs states. Zbl 0834.46049 Hiai, Fumio; Ohya, Masanori; Petz, Dénes 1 1995 Geometry of canonical correlation on the state space of a quantum system. Zbl 0804.53101 Petz, Dénes 40 1994 A survey of certain trace inequalities. Zbl 0802.15012 Petz, Dénes 27 1994 Entropy densities for algebraic states. Zbl 0816.46060 Hiai, Fumio; Petz, Dénes 17 1994 Discrimination between states of a quantum system by observations. Zbl 0808.46096 Petz, Dénes 3 1994 Entropy of Markov states. Zbl 0801.46078 Petz, Dénes 2 1994 On entropy functionals of states of operator algebras. Zbl 0830.46048 Petz, D. 1 1994 Quantum entropy and its use. Zbl 0891.94008 Ohya, Masanori; Petz, Dénes 329 1993 The Golden-Thompson trace inequality is complemented. Zbl 0784.15011 Hiai, Fumio; Petz, Dénes 63 1993 The Bogoliubov inner product in quantum statistics. Zbl 0773.53056 Petz, Dénes; Toth, Gabor 30 1993 Entropy densities for Gibbs states of quantum spin systems. Zbl 0791.60100 Hiai, Fumio; Petz, Dénes 8 1993 Entropies of general quantum states. Zbl 0961.81509 Muraki, Naohumi; Ohya, Masanori; Petz, Dénes 10 1992 Characterization of the relative entropy of states of matrix algebras. Zbl 0765.46045 Petz, D. 8 1992 Entropy in quantum probability. I. Zbl 0824.46073 Petz, Dénes 2 1992 Entropy, the central limit theorem and the algebra of the canonical commutation relation. Zbl 0753.60103 Petz, Dénes 1 1992 The proper formula for relative entropy and its asymptotics in quantum probability. Zbl 0756.46043 Hiai, Fumio; Petz, Dénes 117 1991 ...and 31 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,918 Authors 57 Petz, Dénes 50 Hiai, Fumio 24 Shirokov, Maksim Evgen’evich 23 Wilde, Mark M. 20 Mosonyi, Milán 19 Jenčová, Anna 18 Gyongyosi, Laszlo 17 Datta, Nilanjana 17 Ohya, Masanori 17 Winter, Andreas 16 Molnár, Lajos 16 Tomamichel, Marco 14 Ciaglia, Florio Maria 14 Gibilisco, Paolo 14 Hansen, Frank-Peter 14 Rouzé, Cambyse 14 Ruskai, Mary Beth 14 Watanabe, Noboru 13 Imre, Sandor 13 Mukhamedov, Farruh Maksutovich 12 Audenaert, Koenraad M. R. 12 Berta, Mario 12 Furuichi, Shigeru 12 Isola, Tommaso 12 Luo, Shunlong 12 Slater, Paul B. 11 Accardi, Luigi 11 Benatti, Fabio 11 Carlen, Eric Anders 11 Chafaï, Djalil 11 Guta, Madalin I. 11 Lim, Yongdo 11 Marmo, Giuseppe 11 Seo, Yuki 10 Longo, Roberto 10 Pillet, Claude-Alain 10 Speicher, Roland 10 Ueda, Yoshimichi 10 Wada, Shuhei 10 Życzkowski, Karol 9 Benaych-Georges, Florent 9 Brandão, Fernando G. S. L. 9 Fannes, Mark 9 Jakšić, Vojkan 9 Lewin, Mathieu 9 Osaka, Hiroyuki 9 Rastëgin, Alekseĭ Èduardovich 9 Rougerie, Nicolas 9 Zhang, Lin 8 Chruściński, Dariusz 8 Collins, Benoît 8 Hayashi, Masahito 8 Łuczak, Andrzej 8 Nechita, Ion 8 Szkoła, Arleta 8 Virosztek, Dániel 7 Andai, Attila 7 Di Cosmo, Fabio 7 Feintzeig, Benjamin H. 7 Guionnet, Alice 7 Jiang, Tiefeng 7 Kim, Sejong 7 Lashkari, Nima 7 Lieb, Elliott Hershel 7 Nagy, Gergő 7 Narnhofer, Heide 7 Podsȩdkowska, Hanna 7 Renner, Renato 7 Rouault, Alain 7 Streater, Raymond F. 7 Tam, Tin-Yau 7 Vershynina, Anna 7 Xu, Feng 6 Bebiano, Natália Isabel Quadros 6 Bikchentaev, Aĭrat Midkhatovich 6 Bourin, Jean-Christophe 6 Bryc, Włodzimierz 6 Chistyakov, Gennadiĭ Petrovich 6 Dinh Trung Hoa 6 Fawzi, Omar 6 Fei, Shaoming 6 Gao, Li 6 Girotti, Federico 6 Götze, Friedrich 6 Hollands, Stefan 6 Junge, Marius 6 Kosaki, Hideki 6 Lami, Ludovico 6 Li, Yongtao 6 Naudts, Jan 6 Ogawa, Tomohiro 6 Ohno, Hiromichi 6 Phan Thành Nam 6 Serfaty, Sylvia 6 Sukochev, Fedor Anatol’evich 6 Ugajin, Tomonori 6 Verstraete, Frank 6 Walter, Michael 6 Wolf, Michael Marc 6 Yamazaki, Takeaki ...and 1,818 more Authors all top 5 Cited in 257 Serials 163 Journal of Mathematical Physics 115 Communications in Mathematical Physics 114 Linear Algebra and its Applications 77 Quantum Information Processing 72 Journal of High Energy Physics 66 Journal of Physics A: Mathematical and Theoretical 61 Letters in Mathematical Physics 49 Journal of Functional Analysis 42 Journal of Statistical Physics 38 Reports on Mathematical Physics 38 Infinite Dimensional Analysis, Quantum Probability and Related Topics 36 Annales Henri Poincaré 33 Journal of Mathematical Analysis and Applications 32 International Journal of Quantum Information 28 Physics Letters. A 28 Reviews in Mathematical Physics 28 Probability Theory and Related Fields 27 International Journal of Theoretical Physics 25 Linear and Multilinear Algebra 24 Journal of Theoretical Probability 23 New Journal of Physics 22 Open Systems & Information Dynamics 22 Random Matrices: Theory and Applications 17 Annals of Physics 14 Advances in Mathematics 13 Proceedings of the American Mathematical Society 12 Publications of the Research Institute for Mathematical Sciences, Kyoto University 11 The Annals of Probability 11 International Journal of Mathematics 11 Lobachevskii Journal of Mathematics 11 Journal of Mathematical Inequalities 10 Transactions of the American Mathematical Society 10 Foundations of Physics 9 Problems of Information Transmission 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 9 Information Geometry 8 Physica A 8 The Annals of Statistics 8 Mathematische Zeitschrift 8 Acta Mathematica Hungarica 7 Journal of Geometry and Physics 7 Electronic Journal of Probability 7 Journal of Inequalities and Applications 6 Periodica Mathematica Hungarica 6 Integral Equations and Operator Theory 6 Bernoulli 6 ELA. The Electronic Journal of Linear Algebra 6 Positivity 6 Mathematical Inequalities & Applications 6 Acta Mathematica Sinica. English Series 6 Entropy 6 Physical Review A, Third Series 5 Mathematical Notes 5 Journal of Multivariate Analysis 5 Mathematische Nachrichten 5 Memoirs of the American Mathematical Society 5 Applied Categorical Structures 5 Journal of Mathematical Sciences (New York) 5 Journal of Statistical Mechanics: Theory and Experiment 5 Quantum Studies: Mathematics and Foundations 4 Classical and Quantum Gravity 4 Communications on Pure and Applied Mathematics 4 Israel Journal of Mathematics 4 Physics Reports 4 Theoretical and Mathematical Physics 4 Journal of Approximation Theory 4 Mathematical Physics, Analysis and Geometry 4 Foundations of Computational Mathematics 4 Complex Analysis and Operator Theory 4 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 4 Annals of Functional Analysis 4 Advances in Operator Theory 4 SciPost Physics 3 International Journal of Modern Physics B 3 Physics Letters. B 3 Studia Mathematica 3 Chaos, Solitons and Fractals 3 Archiv der Mathematik 3 Inventiones Mathematicae 3 Journal of Statistical Planning and Inference 3 SIAM Journal on Computing 3 Theoretical Computer Science 3 Advances in Applied Mathematics 3 Physica D 3 SIAM Journal on Matrix Analysis and Applications 3 Proceedings of the National Academy of Sciences of the United States of America 3 Expositiones Mathematicae 3 Mathematical Programming. Series A. Series B 3 Electronic Communications in Probability 3 Physical Review Letters 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 International Journal of Geometric Methods in Modern Physics 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Operators and Matrices 3 Communications in Theoretical Physics 2 Modern Physics Letters B 2 International Journal of Modern Physics A 2 Archive for Rational Mechanics and Analysis 2 Lithuanian Mathematical Journal 2 Fortschritte der Physik ...and 157 more Serials all top 5 Cited in 61 Fields 994 Quantum theory (81-XX) 493 Functional analysis (46-XX) 432 Information and communication theory, circuits (94-XX) 353 Linear and multilinear algebra; matrix theory (15-XX) 341 Probability theory and stochastic processes (60-XX) 324 Operator theory (47-XX) 260 Statistical mechanics, structure of matter (82-XX) 133 Statistics (62-XX) 68 Differential geometry (53-XX) 57 Relativity and gravitational theory (83-XX) 43 Real functions (26-XX) 38 Partial differential equations (35-XX) 35 Computer science (68-XX) 34 Measure and integration (28-XX) 31 Dynamical systems and ergodic theory (37-XX) 29 Combinatorics (05-XX) 23 Numerical analysis (65-XX) 20 Group theory and generalizations (20-XX) 20 Classical thermodynamics, heat transfer (80-XX) 19 Topological groups, Lie groups (22-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Convex and discrete geometry (52-XX) 17 Special functions (33-XX) 16 General topology (54-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 15 Operations research, mathematical programming (90-XX) 14 Category theory; homological algebra (18-XX) 13 Functions of a complex variable (30-XX) 13 Potential theory (31-XX) 13 Mechanics of particles and systems (70-XX) 11 Associative rings and algebras (16-XX) 11 Nonassociative rings and algebras (17-XX) 11 Systems theory; control (93-XX) 9 Integral transforms, operational calculus (44-XX) 9 Geometry (51-XX) 8 Number theory (11-XX) 8 Ordinary differential equations (34-XX) 8 Difference and functional equations (39-XX) 8 Abstract harmonic analysis (43-XX) 7 Algebraic geometry (14-XX) 7 Approximations and expansions (41-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Sequences, series, summability (40-XX) 4 General and overarching topics; collections (00-XX) 4 Mathematical logic and foundations (03-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Algebraic topology (55-XX) 4 Fluid mechanics (76-XX) 4 Optics, electromagnetic theory (78-XX) 3 History and biography (01-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Manifolds and cell complexes (57-XX) 3 Astronomy and astrophysics (85-XX) 3 Biology and other natural sciences (92-XX) 2 General algebraic systems (08-XX) 2 Integral equations (45-XX) 1 \(K\)-theory (19-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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