Performance of the quantum MaxEnt estimation in the presence of physical symmetries

When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be obtained, in a reliable way, by adopting the maximum entropy principle (MaxEnt principle), as an additional criterion, to achieve the least biased estimation. In this paper, we study the performance of the MaxEnt method for quantum state estimation when there is prior information about symmetries of the unknown state. We explicitly describe how to work with this method in the most general case, and we present an algorithm that allows to improve the estimation of quantum states with arbitrary symmetries. Furthermore, we implement this algorithm to carry out numerical simulations estimating the density matrix of several three-qubit states of particular interest for quantum information tasks. We observed that, for most states, our approach allows to considerably reduce the number of independent measurements needed to obtain a sufficiently high fidelity in the reconstruction of the density matrix. Moreover, we analyze the performance of the method in realistic scenarios, showing that it is robust even when the effects of finite statistics and experimental noise are considered.