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).