Information Geometry and its Applications III

Abstract Akio Fujiwara

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Akio Fujiwara  (Osaka University, Japan)
Friday, August 06, 2010, room Hörsaal 1
Geometry of quantum channel manifolds

A quantum channel is a completely positive map that represents a dynamical change of a quantum system. As a natural generalization of the geometry of Berry-Uhlmann's phase, a principal fibre bundle over a manifold of quantum channels is introduced, in which the redundancy of the operator-sum representation is regarded as a fibre. It is demonstrated that this geometry plays an essential role in quantum channel estimation theory that seeks an optimal estimation scheme for an unknown quantum channel.

References:

[1] A. Fujiwara, "Quantum channel identification problem", Phys. Rev. A, vol. 63, 042304 (2001).

[2] A. Fujiwara and H. Imal, "A fibre bundle over manifolds of quantum channels and its application to quantum statistics", J. Phys. A: Math. Theor., vol. 41, 255304 (2008).

Date and Location

August 02 - 06, 2010
University of Leipzig
Augustusplatz
04103 Leipzig
Germany

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Germany
Contact by Email

Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
Italy
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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
RIKEN
Brain Science Institute, Mathematical Neuroscience Laboratory
Japan
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Hungary
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
Hungary
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
Italy
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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