On quantum state observability and measurement
Domenico D Alessandro · Journal of Physics A Mathematical and General · 2003
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite-dimensional quantum control system for which we can influence the dynamics by generating all the unitary evolutions in a Lie group. We investigate to what extent, by an appropriate sequence of evolutions and measurements, we can obtain information on the initial state of the system. We present a system theoretic viewpoint of this problem in that we study the observability of the system. In this context, we characterize the equivalence classes of indistinguishable states and propose algorithms for state identification.