Measurimg polynomial functions of states

In this paper I show that any mth-degree polynomial function of the elements of the density matrix ρ can be determined by finding the expectation value of an observable on m copies of ρ, without performing state tomography. Since a circuit exists which can approximate the measurement of any observable, in principle one can find a circuit which will estimate any such polynomial function by averaging over many runs. I construct some simple examples and compare these results to existing procedures.