  Several methods, known as Quantum Process Tomography, are available to
characterize the evolution of quantum systems, a task of crucial importance.
However, their complexity dramatically increases with the size of the system.
Here we present the theory describing a new type of method for quantum process
tomography. We describe an algorithm that can be used to selectively estimate
any parameter characterizing a quantum process. Unlike any of its predecessors
this new quantum tomographer combines two main virtues: it requires investing a
number of physical resources scaling polynomially with the number of qubits and
at the same time it does not require any ancillary resources. We present the
results of the first photonic implementation of this quantum device,
characterizing quantum processes affecting two qubits encoded in heralded
single photons. Even for this small system our method displays clear advantages
over the other existing ones.
