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

The estimation of the density operator that describe the state of a quantum system, when an informational complete measurement is not available, can be performed, in a reliable way, by adopting the Maximum Entropy principle (MaxEnt) as additional criterion. In this paper, we have studied the efficiency of the MaxEnt method for quantum states estimation when there is prior information about symmetries of the state. We explicitly describe how to implement the algorithm, in the most general case, and implemented it to conduct numerical simulations estimating the density matrix of several three-qubit quantum state of interest. Furthermore, we analyze the performance of the method in realistic quantum information scenarios. We observe that, for most states, this approach allows to considerably reduce the number of independent measurements needed to obtain a sufficiently high fidelity, and it shows to be robust under the presence of typical experimental noises.