Geometry of quantum channel manifolds

  • Akio Fujiwara (Osaka University, Osaka, Japan)
University n.n. Universität Leipzig (Leipzig)


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).

02.08.10 06.08.10

Information Geometry and its Applications III

Universität Leipzig (Leipzig) University n.n. University n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic