The knowledge of the density matrix of a quantum state plays a fundamental role in several fields ranging from quantum information processing to experiments on foundations of quantum mechanics and quantum optics. Recently, a method has been suggested and implemented in order to obtain the reconstruction of the diagonal elements of the density matrix exploiting the information achievable with realistic on/off detectors, e.g. silicon avalanche photo-diodes, only able to discriminate the presence or the absence of light. The purpose of this paper is to provide an overview of the theoretical and experimental developments of the on/off method, including its extension to the reconstruction of the whole density matrix.
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