  A number of problems in quantum state and system identification are
addressed. Specifically, it is shown that the maximum likelihood estimation
(MLE) approach, already known to apply to quantum state tomography, is also
applicable to quantum process tomography (estimating the Kraus operator sum
representation (OSR)), Hamiltonian parameter estimation, and the related
problems of state and process (OSR) distribution estimation. Except for
Hamiltonian parameter estimation, the other MLE problems are formally of the
same type of convex optimization problem and therefore can be solved very
efficiently to within any desired accuracy.
  Associated with each of these estimation problems, and the focus of the
paper, is an optimal experiment design (OED) problem invoked by the Cramer-Rao
Inequality: find the number of experiments to be performed in a particular
system configuration to maximize estimation accuracy; a configuration being any
number of combinations of sample times, hardware settings, prepared initial
states, etc. We show that in all of the estimation problems, including
Hamiltonian parameter estimation, the optimal experiment design can be obtained
by solving a convex optimization problem.
  Software to solve the MLE and OED convex optimization problems is available
upon request from the first author.
