Abstract:
The dynamics of open quantum systems is described by quantum channels, also known as Kraus maps. The geometry of quantum channel sets plays an important role in solving problems in various areas of quantum theory, from quantum information theory to quantum computing and quantum control. This talk describes results on representing quantum channels using orbits of a unitary group acting on a complex Stiefel manifold and examines the geometry of the corresponding factor space. This representation enables the application of Riemannian optimization methods to the analysis of objective functions on quantum channel sets. Particular attention is paid to the absence of local, but not global, extrema for a wide class of objective functionals important in quantum control.
