Joint Seminar on Quantum Information and Technologies

In this work, we demonstrate that any quantum pure state can bereconstructed from, at most, five probability distributions in everyfinite dimension d. These probability distributions are obtained from 5drank-one projective measurements that can be sorted in 5 orthonormalbases. Our method is adaptative only for a null measure set of purestates. Consequently, our fixed set of five orthonormal bases isinformationaly complete in the sense of Flammia-Silberfarb-Caves (2005).We analyze the quality of the reconstruction when errors in theprobability distributions and noise in the pure state preparation areconsidered. We compare our method with the mutually unbiased basesreconstruction. We show that both methods have the same quality ofreconstruction in dimensions four, five, seven and eight when smallerrors are considered. Finally, we reconstruct a quantum state frommeasurements realized in the laboratory.