  An iterative algorithm for state determination is presented that uses as
physical input the probability distributions for the eigenvalues of two or more
observables in an unknown state $\Phi$. Starting form an arbitrary state
$\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to
$\Phi$ or to a Pauli partner. This algorithm for state reconstruction is
efficient and robust as is seen in the numerical tests presented and is a
useful tool not only for state determination but also for the study of Pauli
partners. Its main ingredient is the Physical Imposition Operator that changes
any state to have the same physical properties, with respect to an observable,
of another state.
