This builds on #115 and adds a KrausOperators type which represents an abstract superoperator in the Kraus representation, along with functions to convert to/from the Superoperator and ChoiState types.
I'm opening this as a draft PR as I work through the remaining TODO items:
[x] another type for the Kraus representation
[x] converters back and forth between the 3 types
[x] application methods (e.g. at the very least having multiplication operator between superoperators and density matrices)
[x] test for correctness
[ ] docstrings with doctest-based examples
I had tried to figure out how to convert to KrausOperators directly from sparse superoperators using both KryolovKit and Arnoldi, however it seems tricky to do in general as for an arbitrary superoperator one cannot know a priori what its Kraus rank is without calculating it's eigenvalues. I thought it might work to ask for, say sqrt(dim) largest eigenvalues then check if the smallest of these was close to zero, however apparently Kryolov methods cannot robustly handle finding all eigenvectors associated to degenerate eigenvalues. Thus this method cannot be used to reliabely find the Kraus representation of a superoperator, even when the superoperator has small Kraus rank.
This builds on #115 and adds a KrausOperators type which represents an abstract superoperator in the Kraus representation, along with functions to convert to/from the Superoperator and ChoiState types.
I'm opening this as a draft PR as I work through the remaining TODO items:
I had tried to figure out how to convert to KrausOperators directly from sparse superoperators using both KryolovKit and Arnoldi, however it seems tricky to do in general as for an arbitrary superoperator one cannot know a priori what its Kraus rank is without calculating it's eigenvalues. I thought it might work to ask for, say sqrt(dim) largest eigenvalues then check if the smallest of these was close to zero, however apparently Kryolov methods cannot robustly handle finding all eigenvectors associated to degenerate eigenvalues. Thus this method cannot be used to reliabely find the Kraus representation of a superoperator, even when the superoperator has small Kraus rank.