Dénes Petz

Dénes Petz's AcademicInfluence.com Rankings

Dénes Petz

Mathematics

#4941

World Rank

#6985

Historical Rank

Measure Theory

#1664

World Rank

#2049

Historical Rank

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Mathematics

Why Is Dénes Petz Influential?

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According to Wikipedia, Dénes Petz was a Hungarian mathematical physicist and quantum information theorist. He is well known for his work on quantum entropy inequalities and equality conditions, quantum f-divergences, sufficiency in quantum statistical inference, quantum Fisher information, and the related concept of monotone metrics in quantum information geometry. He proposed the first quantum generalization of Rényi relative entropy and established its data processing inequality.

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Dénes Petz's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Quantum Entropy and Its Use (1993) (957)
The semicircle law, free random variables, and entropy (2006) (741)
Quantum Information Theory and Quantum Statistics (2007) (560)
Monotone metrics on matrix spaces (1996) (447)
The proper formula for relative entropy and its asymptotics in quantum probability (1991) (424)
Quasi-entropies for finite quantum systems (1986) (407)
Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality (2003) (371)
Sufficient subalgebras and the relative entropy of states of a von Neumann algebra (1986) (243)
SUFFICIENCY OF CHANNELS OVER VON NEUMANN ALGEBRAS (1988) (217)
Geometries of quantum states (1996) (199)
An invitation to the algebra of canonical commutation relations (1990) (197)
Quantum f-divergences and error correction (2010) (157)
Monotonicity of quantum relative entropy revisited (2002) (157)
Introduction to Quantum Fisher Information (2010) (123)
Contractivity of positive and trace-preserving maps under Lp norms (2006) (123)
Quasi-entropies for States of a von Neumann Algebra (1985) (123)
Covariance and Fisher information in quantum mechanics (2001) (120)
Geometry of canonical correlation on the state space of a quantum system (1994) (120)
The Golden-Thompson trace inequality is complemented (1993) (117)
Riemannian metrics on positive definite matrices related to means (2008) (98)
Sufficiency in Quantum Statistical Inference (2004) (91)
A simple proof of the strong subadditivity inequality (2004) (89)
Extremal properties of the variance and the quantum Fisher information (2011) (86)
On the Riemannian metric of α-entropies of density matrices (1996) (83)
A survey of certain trace inequalities (1994) (76)
Entropy, von Neumann and the von Neumann Entropy (2001) (72)
Logarithmic energy as entropy functional (1998) (71)
The Bogoliubov inner product in quantum statistics (1993) (69)
Non-Commutative Extension of Information Geometry II (1997) (62)
A variational expression for the relative entropy (1988) (61)
Asymptotics of Varadhan-type and the Gibbs variational principle (1989) (61)
Means of Positive Numbers and Matrices (2005) (53)
Spectral scale of self-adjoint operators and trace inequalities (1985) (53)
Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations (2009) (49)
On asymptotics of large Haar distributed unitary matrices (2003) (49)
On capacities of quantum channels (2008) (45)
A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices (2000) (44)
Complementarity in quantum systems (2006) (43)
Characterizations of the trace (1988) (41)
From f-divergence to quantum quasi-entropies and their use (2009) (40)
Contraction of Generalized Relative Entropy Under Stochastic Mappings on Matrices (1998) (37)
Eigenvalue Density of the Wishart Matrix and Large Deviations (1998) (36)
Structure of Sufficient Quantum Coarse-Grainings (2003) (36)
Numerical Computation of Quantum Capacity (1998) (36)
Extending the Fisher metric to density matrices (2001) (34)
A DUAL IN VON NEUMANN ALGEBRAS WITH WEIGHTS (1984) (34)
Entropies of general quantum states (1992) (33)
Bregman divergence as relative operator entropy (2007) (32)
Stationary quantum source coding (1999) (32)
Free transportation cost inequalities via random matrix approximation (2004) (32)
Sufficiency in quantum statistical inference. A survey with examples (2006) (31)
From quasi-entropy to various quantum information quantities (2012) (29)
Generalizations of Pauli channels (2008) (28)
ON THE CURVATURE OF A CERTAIN RIEMANNIAN SPACE OF MATRICES (1999) (28)
Entropy Densities for Algebraic States (1994) (27)
Large deviations for functions of two random projection matrices (2005) (26)
Properties of the relative entropy of states of von Neumann algebras (1986) (26)
Complementarity and the algebraic structure of four-level quantum systems (2009) (26)
Families of completely positive maps associated with monotone metrics (2012) (25)
Conditional expectation in quantum probability (1988) (24)
Some inequalities for quantum tsallis entropy related to the strong subadditivity (2014) (24)
On certain properties of the relative entropy of states of operator algebras (1991) (23)
Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices (2004) (22)
Point estimation of states of finite quantum systems (2006) (22)
Gaussian Markov triplets approached by block matrices (2009) (21)
Efficient quantum tomography needs complementary and symmetric measurements (2010) (21)
State extensions and a Radon-Nikodým theorem for conditional expectations on von Neumann algebras. (1989) (20)
Ergodic Theorems in Von Neumann Algebras (1984) (20)
Properties of quantum entropy (1985) (19)
A de Finetti-type theorem withm-dependent states (1990) (19)
Means of positive matrices: Geometry and a conjecture ⁄ (2005) (19)
Characterization of the relative entropy of states of matrix algebras (1992) (18)
State tomography for two qubits using reduced densities (2006) (18)
Complementary reductions for two qubits (2006) (18)
Strongly subadditive functions (2010) (17)
INFORMATION-GEOMETRY OF QUANTUM STATES (1998) (17)
Algebraic complementarity in quantum theory (2010) (17)
Optimal quantum-state tomography with known parameters (2012) (17)
Free energy density for mean field perturbation of states of a one-dimensional spin chain (2007) (17)
Completely positive mappings and mean matrices (2010) (16)
Quasi‐Uniform Ergodic Theorems in von Neumann Algebras (1984) (16)
From Relative Entropy to Entropy (1993) (16)
On the equality in Jensen's inequality for operator convex functions (1986) (15)
Entropy Densities for Gibbs States of Quantum Spin Systems (1993) (14)
Classes of conditional expectations over von Neumann algebras (1990) (14)
Quasi-orthogonal subalgebras of 4 × 4 matrices (2007) (14)
Quantum covariance, quantum Fisher information and the uncertainty principle (2007) (14)
Perturbation of Wigner matrices and a conjecture (2003) (13)
Jensen’s inequality for positive contractions on operator algebras (1987) (13)
Free relative entropy for measures and a corresponding perturbation theory (2002) (13)
Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited (2012) (11)
Markov triplets on CCR-algebras (2008) (11)
From quasi-entropy to skew information (2007) (11)
Properties of Free Entropy Related to Polar Decomposition (1999) (11)
Convex Optimization-Based Parameter Estimation and Experiment Design for Pauli Channels (2012) (11)
Discrimination between states of a quantum system by observations (1994) (11)
From quasi-entropy (2010) (10)
Weighted multivariable operator means of positive definite operators (2014) (9)
Matrix Analysis with some Applications (2011) (8)
Monotonicity of quantum relative entropy revisited 1 (2003) (7)
Entropy, the central limit theorem and the algebra of the canonical commutation relation (1992) (7)
Quantum ergodic theorems (1984) (7)
Riemannian geometry on positive definite matrices (2008) (7)
First steps towards a Donsker and Varadhan theory in operator algebras (1990) (7)
McMillan type convergence for quantum Gibbs states (1995) (6)
Maximizing Free Entropy (1998) (6)
Matrix variances with projections (2012) (6)
Erratum: "Quantum f-divergences and error correction" (2017) (6)
Majorization and Singular Values (2014) (6)
Partial subadditivity of entropies (2013) (6)
Complementarity and the algebraic structure of finite quantum systems (2008) (6)
QUANTUM MECHANICS IN AFC*-SYSTEMS (1996) (6)
Some Decompositions of Matrix Variances (2013) (6)
Monotonicity of f-divergences: A review with new results (2010) (5)
THE CURVATURE OF THE BOGOLIUBOV-KUBO-MORI SCALAR PRODUCT ON MATRICES (2008) (5)
Inequalities related to free entropy derived from random matrix approximation (2003) (5)
Conditional SIC-POVMs (2012) (5)
On entropy functionals of states of operator algebras (1994) (5)
A Free Logarithmic Sobolev Inequality on the Circle (2006) (5)
On the function TreH (2002) (5)
Complementarity and state estimation (2010) (5)
A characterization theorem for matrix variances (2013) (5)
Entropy in Quantum Probability I (1992) (5)
Quantum state tomography with finite sample size (2008) (5)
Markov property of Gaussian states of canonical commutation relation algebras (2009) (4)
Erratum: Extremal properties of the variance and the quantum Fisher information (Physical Review A - Atomic, Molecular, and Optical Physics (2013) 87 (032324)) (2013) (4)
A limit relation for entropy and channel capacity per unit cost (2007) (4)
ON THE FUNCTION Tr e H+itK (2002) (3)
Comparison of some methods of quantum state estimation (2005) (3)
Characterization of mean transformations (2012) (3)
State estimation of N-level quantum systems (2006) (3)
EQUILIBRIUM STATES AND THEIR ENTROPY DENSITIES IN GAUGE-INVARIANT C*-SYSTEMS (2004) (3)
Successive iterations and logarithmic means (2013) (2)
A free analogue of the transportation cost inequality on the circle (2005) (2)
John von Neumann and the Theory of Operator Algebras (2011) (2)
A Characterization of the Canonical Centre-Valued Trace in Finite Von Neumann Algebras (1981) (2)
Notes on quantum entropy (2008) (2)
Quantum Source Coding and Data Compression (2007) (2)
Random matrices and asymptotically free relation (2006) (2)
A Panorama of the Hungarian Real and Functional Analysis in the 20Th Century (2006) (1)
Examples of conditional SIC-POVMs (2015) (1)
Functional Calculus and Derivation (2014) (1)
Matrix Means and Inequalities (2014) (1)
BAYESIAN QUBIT STATE ESTIMATION (2006) (1)
Optical Communication Processes (1993) (1)
A NEW PROOF TO CONSTRUCT MULTIVARIABLE GEOMETRIC MEANS BY SYMMETRIZATION (2015) (1)
Hilbert Space Methods for Quantum Mechanics (2010) (1)
Optimal generalized variance and quantum Fisher information (2011) (1)
A new approach to mutual information (2007) (1)
Bayesian Qubit Tomography (2004) (1)
On spectral and central states on Banach algebras (1983) (1)
Postulates for Entropy and Relative Entropy (1993) (0)
On a problem of D. Newman (1978) (0)
Variational Expression of Perturbational Limits (1993) (0)
Book reviews (1987) (0)
Entropic Uncertainty Relations (1993) (0)
Analytic function theory and infinitely divisible laws (2006) (0)
Appendix: Auxiliary Linear and Convex Analysis (2008) (0)
Convex Trace Functions (1993) (0)
Probability laws and noncommutative random variables (2006) (0)
Variation of Heisenberg uncertainty relation involvingaverage (2017) (0)
Functionals of Entropy Type (1993) (0)
COMPLEMENTARY SUBALGEBRAS IN FINITE QUANTUM SYSTEMS (2011) (0)
Thermodynamics of Quantum Spin Systems (1993) (0)
SATURATION OF AN ENTROPY BOUND AND QUANTUM MARKOV STATES (2006) (0)
D ec 2 00 8 Markov triplets on CCR-algebras (0)
QUASr-ENTROPTES FOR FTNTTE QUANTUM SYSTEMS (1984) (0)
On box products of syntopogenous spaces (1980) (0)
GAUSSIAN MARKOV TRIPLETS (2010) (0)
The free relation (2006) (0)
Quantum source coding and data compression 1 (2004) (0)
More About Information Quantities (2008) (0)
Fundamentals of Operators and Matrices (2014) (0)
Positive mappings on matrix algebras (1989) (0)
Modular Theory and Auxiliaries (1993) (0)
Means of positive numbers and matrices 1 Dedicated to Professor Pál Rózsa on the occasion of his 80 th birthday (0)
Central Limit and Quasi-free Reduction (1993) (0)
Structure of sufficient quantum coarse-grainings 1 (0)
Mappings and Algebras (2014) (0)
PR ] 1 O ct 2 00 4 Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices 1 (2004) (0)
Information and its Measures (2008) (0)
Channels and Their Capacity (2008) (0)
Examples of conditional SIC-POVMs (2015) (0)
Book review (1983) (0)
Almost uniform convergence on the predual of a von Neumann algebra and an ergodic theorem (1986) (0)
Sufficient Channels and Measurements (1993) (0)
FA ] 1 8 D ec 2 00 7 From quasi-entropy to skew information (2021) (0)
Matrix Monotone Functions and Convexity (2014) (0)
Foreword (2008) (0)
Book review (1979) (0)
Chain rules for canonical state extensions on von Neumann algebras (1993) (0)
Fe b 20 12 Conditional SIC-POVMs (2012) (0)
Temperley-Lieb Algebras and Index (1993) (0)
Perturbation of States (1993) (0)
Relative Entropy of States of Operator Algebras (1993) (0)
Channels and Their Transpose (1993) (0)
Prerequisites from Quantum Mechanics (2008) (0)
Relation to operator algebras (2006) (0)
O ct 2 00 6 Complementarity in Quantum Systems (2008) (0)
Free entropy of noncommutative random variables (2006) (0)

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Other Resources About Dénes Petz

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What Schools Are Affiliated With Dénes Petz?

Dénes Petz is affiliated with the following schools:

Budapest University of Technology and Economics