  The principle of maximum likelihood reconstruction has proven to yield
satisfactory results in the context of quantum state tomography for many-body
systems of moderate system sizes. Until recently, however, quantum state
tomography has been considered to be infeasible for systems consisting of a
large number of subsystems due to the exponential growth of the Hilbert space
dimension with the number of constituents. Several reconstruction schemes have
been proposed since then to overcome the two main obstacles in quantum
many-body tomography: experiment time and postprocessing resources. Here we
discuss one strategy to address these limitations for the maximum likelihood
principle by adopting a particular state representation to merge a well
established reconstruction algorithm maximizing the likelihood with techniques
known from quantum many-body theory.
