  We propose a refined iterative likelihood-maximization algorithm for
reconstructing a quantum state from a set of tomographic measurements. The
algorithm is characterized by a very high convergence rate and features a
simple adaptive procedure that ensures likelihood increase in every iteration
and convergence to the maximum-likelihood state.
  We apply the algorithm to homodyne tomography of optical states and quantum
tomography of entangled spin states of trapped ions and investigate its
convergence properties.

Quantum Physics