Estimation of Pure States Using Three Measurement Bases
Leonardo Zambrano, L. Pereira, Daniel Martínez, Gustavo Cañas, Gislayne Karen dos Santos Lima, A. Delgado · Physical Review Applied · 2020
We introduce a method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. The measurement results of $2d$ projectors are used to generate a set of ${2}^{d\ensuremath{-}1}$ states, the value of the likelihood function of which is evaluated using the measurement results of the remaining $d$ projectors. The state with the highest value of the likelihood function is the estimate of the unknown state. The method estimates all pure states except for a null-measure set, which can be overcome by adapting two bases. The viability of the protocol is experimentally demonstrated using two different and complementary high-dimensional quantum information platforms. First, by exploring the photonic path-encoding strategy, we validate the method on a single eight-dimensional quantum system. Then, we resort to the five-superconducting-qubit IBM quantum processor to demonstrate the high performance of the method in the multipartite scenario.