On the observability and state determination of quantum mechanical systems

We consider the problem of determining the state of a quantum system via a series of controlled evolutions and nonselective measurements of a given observable. Generalizing previous results to the case of possibly degenerate observables, we give a bound on the maximum number of parameters of the state that can be determined. We give a general algorithm for the determination of the maximum number of parameters. We also discuss how indirect measurement, when the system and probe are jointly controllable, allows one to determine all the parameters of the quantum state