Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups

Given a quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be computed. These methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography-the statistical estimation of superoperators and their generators-from a wide variety of experimental data. Theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data. (C) 2003 American Institute of Physics.