Direct estimations of linear and nonlinear functionals of a quantum state

Phys Rev Lett. 2002 May 27;88(21):217901. doi: 10.1103/PhysRevLett.88.217901. Epub 2002 May 13.


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 as a basic building block for direct quantum estimations of both linear and nonlinear 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.