Quantum tomography via unambiguous state discrimination
Roberto Salazar, A. Delgado · Physical Review A · 2012
We study the determination of an unknown mixed state of a $d$-dimensional quantum system by means of unambiguous state discrimination. We show that optimal and nonoptimal unambiguous state discrimination can be used to reconstruct unknown states of a qubit. This result is extended to the case of a qudit by a sequence of reconstructions in two-dimensional subspaces. The total number of projections scales approximately as $2{d}^{2}$ for $d$ large; this is twice as much as in the case of tomography based on mutually unbiased bases or symmetric informationally complete positive-operator-valued measures, and less than the ${d}^{3}$ projections required by standard tomography.