Fidelity and channels in semifinite von Neumann algebras
Density operators and quantum channels have very precise definitions in the context of finite-dimensional Hilbert space: they are positive operators of unit trace, in the former case, and trace-preserving completely positive linear maps, in the latter case. But how do these definitions apply in the context of infinite-dimensional space? To a certain extent, this has already been worked out by Kraus in his classic 1970 paper on states and effects. More generally, though, how do these definitions apply in the setting of semifinite von Neumann algebras? The first part of the lecture will address this question.
The second part of the lecture concerns the notion of fidelity and a study of how fidelity is altered by a quantum channel.
This lecture is based on joint work with Sam Jaques and Miza Rahaman.