Reconstructing quantum states via unambiguous state discrimination

Abstract In this paper, we introduce an analytical framework for the reconstruction of quantum states. The reconstruction of an unknown quantum state requires the information of a complete set of observables, obtained through experimental measurements of Hermitian operators usually defined as positive-operator-valued measures (POVMs). The scheme involves a single-qubit unambiguous state discrimination POVM, which can be generalized to perform n-qubit measurements. We also use maximum likelihood estimation as a method in the reconstruction of the density matrix from experimental data and show that the expected value of the cleaner is independent of the parameter of the density operator.