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.


[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
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