  We present a simple quantum network, based on the controlled-SWAP gate, that
can extract certain properties of quantum states without recourse to quantum
tomography. It can be used used as a basic building block for direct quantum
estimations of both linear and non-linear functionals of any density operator.
The network has many potential applications ranging from purity tests and
eigenvalue estimations to direct characterization of some properties of quantum
channels. Experimental realizations of the proposed network are within the
reach of quantum technology that is currently being developed.
