Efficient quantum-state tomography for quantum-information processing using a two-dimensional Fourier-transform technique

A method of quantum-state tomography for quantum-information processing is described. The method is based on the use of the Fourier-transform technique and involves detection of all the diagonal elements of the density matrix in a one-dimensional experiment and all the off-diagonal elements by a two-dimensional experiment. The method is efficient for a large number of qubits $(>~5).$ The proposed method is outlined using a two-qubit system and demonstrated using simulations by tomographing arbitrary complex density matrices of two- and four-qubit systems.