Optimizing measurements sequences for quantum state verification

We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate; namely, it produces states close to a target one within a prescribed threshold. While most of the result in the literature considers the case in which the measurement operators can be arbitrarily chosen depending on the target state, obtaining favorable (Heisenberg) scaling, we focus on the case in which the measurements can be only chosen from a given set. We show that, in this case, the order of measurements is critical for quickly assessing accuracy. We propose and compare different strategies to compute optimal or suboptimal measurement sequences either relying solely on a priori information, i.e., the target state for state preparation, or actively adapting the sequence to the previously obtained measurements. Numerical simulations show that the proposed algorithms reduce significantly the number of measurements needed for verification and indicate an advantage for the adaptive protocol especially assessing faulty preparations.