Information Geometry and its Applications III

Abstract Paolo Gibilisco

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Paolo Gibilisco  (Università degli Studi di Roma "Tor Vergata", Italy)
Friday, August 06, 2010, room Hörsaal 2
The formula3 correspondence and its applications in quantum information theory

Let formula52={symmetric, normalized, operator monotone functions}. If we set
trivially it holds
It is possible to prove that the map formula56 is a bijection from formula58 to formula60, namely a bijection between regular and non-regular functions.

In the last years a number of consequences has been derived from this fact: 1) the dynamical uncertainty principle; 2) its generalization to von Neumann algebras; 3) a new proof of the fact that the Wigner-Yanase-Dyson is an example of a quantum Fisher information; 4) a new proof the monotonicity property for the WYD information; 5) a link between quantum relative entropy and metric adjusted skew information.

The purpose of my talk is to describe the above applications.

  • Andai, A., Uncertainty principle with quantum Fisher information, J. Math. Phys. 49 (2008), 012106.
  • Audenaert, K., Cai, L. and Hansen, F., Inequalities for quantum skew information, Lett. Math. Phys., 85: 135-146, 2008.
  • Gibilisco, P., Hansen, F. and Isola T., On a correspondence between regular and non-regular operator monotone functions. Linear Algebra Appl., 430: 2225-2232, 2009.
  • Gibilisco, P., Hiai F. and Petz, D., Quantum covariance, quantum Fisher information and the uncertainty relations. IEEE Trans. Inform. Theory, 55: 439-443, 2009.
  • Gibilisco, P. and Isola, T., A dynamical uncertainty principle in von Neumann algebras by operator monotone functions. J. Stat. Phys., 132: 937-944, 2008.
  • Luo, S., Quantum Fisher information and uncertainty relations. Lett. Math. Phys. 53: 243-251, 2000.
  • Petz, D. and Szabó, V. E. S., From quasi-entropy to skew information. International J. Math., 20:1421-1430, 2009.

Date and Location

August 02 - 06, 2010
University of Leipzig
04103 Leipzig

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
Brain Science Institute, Mathematical Neuroscience Laboratory
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42