Selective and efficient quantum state tomography and its application to quantum process tomography

We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is written can be efficiently prepared in a controlled manner. Furthermore, we show how this algorithm is well suited for quantum process tomography, enabling one to perform selective and efficient quantum process tomography.