Professional activities of Dénes Petz

Ruth Bloch: Entanglement
(bronze, 71 cm, 1995)

Research interest

Mathematical  physics, linear analysis, free probability, mathematical foundations of quantum theory, quantum information theory.


D. Petz,  An invitation to the algebra of the canonical commutation relation, Leuven University Press, Leuven, 1990.

M. Ohya and D. Petz, Quantum Entropy and Its Use, Springer-Verlag, Heidelberg, 1993. Second edition 2004.

F. Hiai and D. Petz, The semicircle law, free random variables and
entropy, American Mathematical Society, Providence, 2000

Petz Dénes, Lineáris Analízis (in Hungarian), Akadémiai Kiadó, Budapest, 2002.

D. Petz, Quantum information theory and quantum statistics, Springer, 2008.


Editorial work

Editor of  Open Systems & Information Dynamics
Editor of  Infinite Dimensional Analysis, Quantum Probability and Related Topics
Editor of   Studia Mathematica Hungarica
Editor of   Linear and Multilinear Algebra
Associate editor of Periodica Mathematica Hungarica

Membership in scientific committees

6th Central European Quantum Information, 1-4 June, 2009,  member  of  Program  Committe
11th workshop on Non-commutative Harmonic Analysis with Applications to Probability, August 17-23,  2008, Bedlewo, Poland, member  of Scientific Committe
QUANTUM PROBABILITY, INFORMATION AND CONTROL SYMPOSIUM, Nottigham 15-22 July, 2006,  member  of Scientific Advisary Committe
Quantum Probability, Greiswald, March 27-31 2006, member  of Scientific Committe
8th WORKSHOP: NON-COMMUTATIVE HARMONIC ANALYSIS, Bedlewo, 2005, member  of Scientific Committe
Fejér-Riesz conference, Eger, 2005, member of Program Committe


Leuven Mathematical Physics Days, 6-7 May, 2010, Belgium, invited speaker
Information Geometry and its Applications, August 02 - 06, 2010. Leipzig, scientifc committee member
Dissipative Systems: Entropy Methods, Classical and Quantum Probability, November 1-3, 2010, Wien, keynote speaker
Summer School and Advanced Workshop on Trends and Developments in Linear Algebra June 22 - July 10, 2009, Trieste, Italy, invited speaker
30th Conference on Quantum Probability, November 23-28, 2009, Santiago, Chile, invited speaker
Workshop on Statistical-Mechanical Informatics 2008, September 14-17, 2008, Sendai, Japan, invited speaker
Quantum Statistical Physics and Quantum Information TheoryApril 21 - 25, 2008, University of Cergy-Pontoise, invited speaker
28-th Conference on Quantum Probability and Related TopicsCIMAT-Guanajuato, MEXICO, 2-8 September 2007, invited spaker
Perspectives in theory and technology of quantum information and communicationMarch 5 to 9th, 2007, Marseille, invited spaker
School on Theory and Technology in Quantum Information, Communication, Computation and Cryptography,  June, 2006, Trieste, invited speaker
Quantum Entanglement & Geometry, Toruń, June 4-7, 2006, invited speaker
 IGAIA2,   December 12-16, 2005, University of Tokyo, invited speaker
4th Sendai Workshop Free probability and random matrices, October 10-12, 2005, invited speaker
Mathematical Physics Days. Leuven, September 12-14, 2005, invited speaker
Philosophical and Foundational Issues in Quantum Theory , Budapest September 1-5, 2005, invited speaker
Free Probability Theory , March 27 - April 2, 2005, Oberwolfach, invited speaker
Free Probability (Banf, 2004),  invited speaker

Selected publications

D. Petz, A characterization of the canonical centre-valued trace in finite von Neumann algebras, J. London Math. Soc. 23(1981), 329-331.
D. Petz, Quasi-uniform ergodic theorems in von Neumann algebras, Bull. London Math. Soc. 16(1984), 151--156.
D. Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra, Commun. Math. Phys. 105(1986), 123-131.
D. Petz, Jensen's inequality for contractions on operator algebras, Proc. Amer. Math. Soc., 99(1987), 273--277.
C. Cecchini and  D. Petz, State extensions and a Radon-Nikodym theorem for conditional expectations on von Neumann algebras, Pacific J. Math.,  138(1989), 9-24.
D. Petz, A de Finetti-type theorem with m-dependent states, Prob. Th. Rel. Fields, 85(1990), 1-11.
F. Hiai and  D. Petz,The proper formula for relative entropy and its asymptotics in quantum probability, Commun. Math. Phys. 143(1991), 99-114.
D. Petz, Discrimination between states of a quantum system by observations, J. Functional Anal. 120(1994), 82-97.
D. Petz, Monotone metrics on matrix spaces, Linear Algebra Appl. 244(1996), 81-96.
M. Ohya, D. Petz and  N. Watanabe, On capacities of quantum channels, Prob. Math. Stat. 17(1997), 179-196.
F. Hiai and D. Petz, A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices, Ann. Inst. Henri Poincaré, Probabilités et Statistiques 36(2000), 71-85.
M. Fannes and D. Petz, Perturbation of Wigner matrices and a conjecture,  Proc. Amer. Math. Soc. 131(2003), 1981-1988.
P. Hayden, R. Jozsa, D. Petz and A. Winter, Structure of states which  satisfy strong subadditivity of quantum entropy with equality, Commun. Math. Phys. 246(2004), 359-374


Koenraad Audenaert, Attila Andai, Tsuyoshi Ando, Nobuyuki Akiho, Thomas Baier, Cedric Beny, Ádám Besenyei, Carlo Cecchini, Ákos Császár, Imre Csiszár, Mark Fannes, D. Perez-Garcia, Katalin M. Hangos, Hiroshi Hasegawa, Patrick Hayden, Fumio Hiai, Anna Jencova, Richard Jozsa, Veronika Kovács, Attila Magyar, Peter W. Michor, M Mizou, Milán Mosonyi, M. Muraki, Michael Nielsen, Masanori Ohya, Hiromichi Ohno, Ferenc Oravecz, József Pitrik, Júlia Réffy, Mary Beth Ruskai, Csaba Sudár, Guido Raggio, Miklós Rédei, András Szántó, Gábor J. Székely, Ferenc Szöllősi, Róbert Temesi, Gábor Tóth, Yoshimichi Ueda, André Verbeure, Noboru Watanabe,  Mihály Weiner, Andreas Winter,  M.M. Wolf,  Jaroslav Zemánek