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We present the results of the first photonic implementation of a new method for quantum process tomography. The method {originally presented by A. Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)10.1103/PhysRevLett.100.190403]} enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones, and its advantages are discussed.

Selective and Efficient Quantum Process Tomography with Single Photons