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.
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