Estimation of pure states using three measurement bases
We introduce a new method to estimate unknown pure $d$-dimensional quantum
states using the probability distributions associated with only three
measurement bases. Measurement results of $2d$ projectors are employed to
generate a set of $2^{d-1}$ possible states, the likelihood of which is
evaluated using the measurement results of the $d$ remaining projectors. The
state with the highest likelihood is the estimate of the unknown state. The
method estimates all pure states but a null-measure set. 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
8-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.
L. Zambrano L. Pereira D. Martínez G. Cañas G. Lima A. Delgado