Estimation of pure states using three measurement bases
Abstract
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 2d-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.