  In this paper I show that any $m$th-degree polynomial function of the
elements of the density matrix $\rho$ can be determined by finding the
expectation value of an observable on $m$ copies of $\rho$, 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.
